The horn goes off when I try to flash my high beams (the light switch is in the "off" position). Also my low beams don't work, however my high beams do works fine.

The headlamps are controlled by the BCM - body control module , do you know what that is ? The headlamp switch is a input to the BCM ,the BCM energizes relays to turn on the headlmps , low beam relay , high beam relay , DRL relay . These relay's are PCB - printed circuit board relay's ( non - serviceable ) If found to be bad the whole under hood fuse box would need to be replaced .
Low Beam Headlamp Operation
The low beam headlamps may be turned ON in 3 different ways:
• When the headlamp switch in the HEAD position for normal operations
• When the headlamp switch is in the AUTO position, for automatic lamp control (ALC)
• When the headlamp switch is placed in the AUTO position, with the windshield wipers ON in daylight conditions, after a 6 second delay
Battery voltage is applied at all times to the coil and switch sides of the LOW BEAM PCB Relay located in the underhood fuse block. When the headlamp switch is placed in the HEAD position, ground from G202 is applied through headlamps ON switch signal circuit to the body control module (BCM), signaling the headlamps ON request. In response to this signal, the BCM applies ground through the headlamp low beam relay control circuit energizing the low beam relay. With the relay energized, battery voltage is applied through the switch side of the relay, the left and right low beam fuses, and the low beam supply voltage circuits illuminating the low beam headlamps. Ground for the left headlamp is provided at G101 and the right headlamp at G100.

Do you know what B codes are ? BCM - DTC'S - diagnostic trouble codes , need a factory scanner or professional one to view these codes , not autozone or advance etc....Having a qualified repair shop check your vehicle would be your best bet.

DTC B2575 00: Headlamp Control Circuit

Circuit/System Description
The vehicle headlamps are controlled by the body control module (BCM) based on inputs from the headlamp switch and the turn signal/multifunction switch. The headlamp switch has four positions: Off, Auto, Park, and Headlamps. The default headlamp switch position is Auto, in which the BCM uses the ambient light sensor to determine when headlamps are needed. The Off portion of the headlamp switch is a momentary switch which overrides the automatic headlamps and will turn off the vehicle headlamps. When in the Off position, the headlamp switch grounds the headlamp switch headlamps off signal circuit, prompting the BCM to turn off the headlamps. The Park position of the headlamp switch will only illuminate the vehicle parking lamps. The Headlamp position of the headlamp switch will illuminate both the parking lamps, as well has the headlamps. With the headlamp switch in the Headlamp position, the headlamp switch headlamps on signal circuit is grounded, prompting the BCM to turn on the headlamps, regardless of other factors such as ambient light.
The headlamp high beams are controlled through the flash to pass switch and the headlamp dimmer switch, both located in the turn signal/multifunction switch. The flash to pass switch is a momentary type switch, designed to illuminate the high beams as long as the switch is held. With the switch closed, the flash to pass switch signal circuit is grounded, prompting the BCM to turn on the high beam lamps. The headlamp dimmer switch allows the operator to select between full time high or low beam operation. Unlike the flash to pass switch, it is not a momentary switch. When the headlamp dimmer switch is in the high beam position, the headlamp dimmer switch high beam signal circuit is grounded. This prompts the BCM to turn on the high beam lamps.
The BCM controls the headlamps based on the inputs explained above. When a low beam request is received, the BCM grounds the headlamp low beam relay control circuit. This energizes the coil in the LOW BEAM PCB relay, causing the relay switch to close. This then applies B+ to both low beam headlamps through the LT LO BEAM and RT LO BEAM fuses, illuminating the low beam headlamps. When a high beam request is received, the BCM grounds the headlamp high beam relay control circuit. This energizes the coil in the HIGH BEAM PCB relay, causing the relay switch to close. This then applies B+ to both high beam headlamps through the LT HI BEAM and RT HI BEAM fuses, illuminating the high beam headlamps

Here is how they are suppose to work .
Headlamps
The headlamps may be turned on two different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the OFF position, for automatic lamp control (ALC). During ALC, the headlamps will be in day time running lamp (DRL) operation in daylight conditions, or low beam operation in low light conditions. The LH HDLPand RH HDLP fuses, supply battery positive voltage from the underhood junction block to the left and right headlamps. The circuit continues through both low and high beam lamps, then back to the underhood junction block. The low beam and high beam circuits continue to the headlamp switch. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer switch and the flash-to-pass switch. When the headlamp switch is placed in the HEADLAMP position a path to ground is provided. Ground is provided at G201. Depending on the position of the high/low beam switch, either the low or high beam circuit will now have power and ground.
The LH HDLP fuse in the underhood junction block, supplies battery positive voltage to the automatic lamp control (ALC) headlamp relay coil circuit. The ALC relay switch circuit is connected to the low beam circuit at the headlamp switch. When the headlamp switch is placed in the OFF position, the BCM will automatically turn on the low beams in low light conditions. The BCM energizes the ALC relay, closing the switch contacts and grounding the low beam circuit. Ground is provided at G201. With the headlights in the low beam position, the high beams may be momentarily turned on or flashed with the dimmer switch handle. The flash-to-pass feature is accomplished by pulling the dimmer switch handle toward the driver. The headlights may be switched to high beam with the opposite movement of the dimmer switch lever. When the headlamp dimmer switch handle is pulled toward the driver, the flash-to-pass switch closes grounding the high beam circuit. Ground is provided at G201. Both high beams will remain on until the driver releases the switch handle.
If the driver places the headlight switch in the HEADLAMP position , the headlights will remain on until turned off or the battery runs dead.

Finding a wiring diagram to use along with a DMM - digital multi-meter (voltmeter ) To test the electrical circuits for the headlamps B+ power & ground side of the circuit is the way to find a fix .
Watching a few basic electrical testing video's on youtube may help you .
Basic Electricity for Service Techs Ohm law Current Flow Opens Shorts
How to Use Multimeter to Troubleshoot Common Problems
The Trainer 18 Electrical Testing Tips
Can take years to learn how to trouble shoot automotive electrical systems properly .

It is normal that when you select high beam that the two high beam lights come on and the low beams switch off. the light position should show high beam
It goes off on low beam when the high beam lights go off and the low beams light up
If the light is reversed then check the wiring to the light
You didn't mention what car it is but if it has a light module then the problem may be in it.

Which insturment cluster does your's have ? electronic instrument cluster or standard instrument cluster !

Standard insturment cluster - speedo / odometer
Speedometer/Odometer
The speedometer and odometer provides speed information based on a speed/distance pulse signal from the vehicle speed sensor (VSS). The VSS is mounted on the speedometer driven gear in the transmission.
Could be the VSS is bad .
Horn The horn system includes the following:

• horn relay
• horn
• clock spring
• steering wheel control switch harness
• steering wheel pad horn switch, which is part of the driver side air bag module. For additional information, refer to Section 501-20B .

The horn is located behind the front bumper mounted to the radiator support.

Is the air bag light lit on the insturment cluster ? If it is the clock spring could be the problem . If not lit check the circuits from the horn relay .

VEHICLE RELAYS Operation Diagnosis .

Which headlamps don't work ? Low beams , high beams , both ?

• The high beams are inoperative

• Bulbs.
• Circuitry.
• Multifunction switch.

• GO to Pinpoint Test C .

• The low beams are inoperative

• Bulbs.
• Circuitry.
• Headlamp switch.
• Multifunction switch.
• LCM.

• GO to Pinpoint Test D .

Principles of Operation
NOTE: Due to varying wattage ratings and resulting current draw, certain aftermarket headlamp bulbs may cause the lighting control module (LCM) to shut down the short circuit protection, resulting in the low beams becoming inoperative. Verify that the headlamp bulbs meet Ford specifications.
Headlamp System The headlamp system consists of:

• two aerodynamic halogen headlamp bulbs and retainers
• headlamp switch
• multifunction switch
• lighting control module (LCM)
• circuit wiring and circuit protection

In normal operation:

• With the multifunction switch in the low beam position, power is supplied by the LCM to the low beam elements through the multifunction switch.
• With the multifunction switch in the high beam position (forward detent), power is supplied to the high beam elements and to the high beam indicator in the instrument cluster.
• When the multifunction switch is pulled toward the steering wheel, the flash-to-pass switch (part of the multifunction switch) is closed and power is supplied to the high beam elements. When the switch is released, they return to low beam operation.
• The battery saver feature of the LCM will automatically turn off the courtesy lamps, demand lamps, headlamps, or parking lamps under the following conditions:
  • The ignition switch is in the OFF position.
  • The headlamp switch is in parking lamps ON or headlamps ON positions.
  • After 10 minutes.

Headlamp Switch The headlamp switch is a multi-position switch.

• The positions include OFF, PARK, and HEAD.
• With the headlamp switch in the PARK position (first detent), a signal is supplied to the LCM which powers the front parking lamps, the tail lamps, the side marker lamps, and the license lamp.
• With the headlamp switch in the HEAD position, power is supplied to the headlamps through the LCM and the multifunction switch.
• The panel dim switch (part of the headlamp switch) is located above the headlamp switch. The panel dim switch operates only with the parking lamps or headlamps on.
• When the panel dim switch is held in the up position, the instrument panel lighting will progressively brighten.
• When the panel dim switch is held in the down position, the instrument panel lighting will progressively dim.

For additional information, refer to Section 413-00 .
Headlamps On Warning Chime If the headlamp switch is left in either the PARK or HEAD position and the driver door is opened, the LCM will sound a headlamps on reminder chime when the following conditions occur:

• The ignition switch is OFF with the ignition key out.
• The driver door is ajar.

For additional information, refer to Section 413-09 .

Inspection and Verification

1. Verify the customer concern by operating the system.

1. Visually inspect for obvious signs of mechanical and electrical damage.

Visual Inspection Chart Mechanical Electrical

• Headlamp switch

• Central junction box (CJB) fuse(s):
  • 6 (15A)
  • 15 (15A)
  • 21 (15A)
  • 23 (15A)
  • 27 (20A)
• Battery junction box (BJB) HI-BEAM HEADLIGHTS (20A) fuse
• Circuitry
• Headlamp bulb
• Lighting control module (LCM)
• Loose or corroded connections

Not a fuse problem , same fuse power's low an high beams . Looking at wiring diagrams an using a DVOM - digital volt ohm meter to test the electrical circuit's is the way to find the problem . The light's staying on for 3 or 4 min's. is a function of the BCM - body control module ! Do you know anything about automotive electrical testing ? Do you know what a wiring diagram is an how to read one . Free wiring diagrams here http://www.bbbind.com/free_tsb.html Enter vehicle info. Year , make , model an engine size . Under system click on lighting ,then under subsystem click on headlamps .Click the search button then the blue link. get yourself a cheap DVOM an test the electrical circuit's , this is how electrical problems are solved .
Electric Testing Techniques You Need to Know
Basic Electricity for Service Techs Ohm law Current Flow Opens Shorts

Plus reading factory service repair info for how it should work would be a good idea .

Headlamps
The headlamps may be turned on two different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the OFF position, for automatic lamp control (ALC). During ALC, the headlamps will be in day time running lamp (DRL) operation in daylight conditions, or low beam operation in low light conditions. The LH HDLPand RH HDLP fuses, supply battery positive voltage from the underhood junction block to the left and right headlamps. The circuit continues through both low and high beam lamps, then back to the underhood junction block. The low beam and high beam circuits continue to the headlamp switch. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer switch and the flash-to-pass switch. When the headlamp switch is placed in the HEADLAMP position a path to ground is provided. Ground is provided at G201. Depending on the position of the high/low beam switch, either the low or high beam circuit will now have power and ground.
The LH HDLP fuse in the underhood junction block, supplies battery positive voltage to the automatic lamp control (ALC) headlamp relay coil circuit. The ALC relay switch circuit is connected to the low beam circuit at the headlamp switch. When the headlamp switch is placed in the OFF position, the BCM will automatically turn on the low beams in low light conditions. The BCM energizes the ALC relay, closing the switch contacts and grounding the low beam circuit. Ground is provided at G201. With the headlights in the low beam position, the high beams may be momentarily turned on or flashed with the dimmer switch handle. The flash-to-pass feature is accomplished by pulling the dimmer switch handle toward the driver. The headlights may be switched to high beam with the opposite movement of the dimmer switch lever. When the headlamp dimmer switch handle is pulled toward the driver, the flash-to-pass switch closes grounding the high beam circuit. Ground is provided at G201. Both high beams will remain on until the driver releases the switch handle.
If the driver places the headlight switch in the HEADLAMP position , the headlights will remain on until turned off or the battery runs dead.
Do you know what a factory diagnostic trouble shooting chart is ?

Headlamps Inoperative - Low Beams

Step
Action
Yes
No
Schematic Reference: Headlights/Daytime Running Lights (DRL) Schematics
1
Did you perform the Lighting System Diagnostic System Check?
YES - Go to Step 2
NO - Go to Diagnostic System Check - Lighting Systems
2
Place the headlamp switch in the HEADLAMP position.
Place the headlamp dimmer switch in the LOW position.
Do the low beam headlamps illuminate?
YES - Go to Testing for Intermittent Conditions and Poor Connections in Wiring Systems
NO - Go to Step 3
3
Disconnect the turn/headlamp wiper switch assembly connector C2.
Connect a 15 amp fused jumper between the headlamp low beam signal circuit and a good ground.
Do the low beam headlamps illuminate?
YES - Go to Step 4
NO - Go to Step 5
4
Inspect for poor connections at the harness connector of the turn/headlamp wiper switch assembly. Refer to Testing for Intermittent Conditions and Poor Connections and Connector Repairs in Wiring Systems.
Did you find and correct the condition?
YES - Go to Step 7
NO - Go to Step 6
5
Repair an open or high resistance in the headlamp low beam signal circuit. Refer to Circuit Testing and Wiring Repairs in Wiring Systems.
YES - Did you complete the repair?
NO - Go to Step 7
--
6
Replace the turn/headlamp wiper switch assembly. Refer to Multifunction Turn Signal Lever Replacement - On Vehicle in Steering Wheel and Column.
Did you complete the replacement?
Go to Step 7
--
7
Operate the system in order to verify the repair.
Did you correct the condition?
YES - System OK
NO - Go to Step 3

If the bulbs flash when you unlock the vehicle, then they are likely not the issue. My guess is the relay contacts are dirty. Just because a relay clicks, it doesn't mean that it is passing current through the contacts. Try and swap the relay with another of the exact same part number. There's usually another available...ie the horn relay, fog lamp etc..

Your running lights which come on when you are in drive should be the ones flashing when you use the key FOB to lock or unlock vehicle not your head lights. Although unusual maybe both low beam head lights are burnt out or a bad ground, that the only thing that makes sense to me.

check your fuse box

I would start with checking the headlight bulbs (slim to none possibility but starting point) next go to the headlight switch.

When you switch from High to Low beams, do the lights go out, or continue, in the "High" beam position??? If they go go, the transfer switch, that changes the high/low beam mode is working. The most likely problem, is that the Low Beam filaments are both burned out. Some, on original equipment, never changed, can burn out within days/weeks of each other. Could be that.