Front driver's side signal light does not work. Changed the bulb and it still does not work. The driver's side rear works and the passenger side works (front and back). Also, when the signal arm is pushed down for the left turn it clicks faster than the right turn.

Did you replace the bulb in the passenger side running light/turn signal socket? There are two filaments in that bulb, one for the running light (which you indicate works) and one for the turn signal. If that bulb (filament) is burned out, it will make the turn signal flash faster. I don't know why you were swapping headlights, don't know where the fire box under the hood is, and don't know what a jumper sore is, so can't help you any further. I have a Saturn Ion, and have never found a fire box or jumper sore in it.

Circuit/System Description
Ground is applied at all times at G201 to the turn signal/multifunction switch. The turn signal lamps may only be activated with the ignition switch in the ON or START position. When the turn signal/multifunction switch is placed in either the TURN RIGHT or TURN LEFT position, ground is applied to the body control module (BCM) through either the right turn or left turn signal switch signal circuit. The BCM then applies a pulsating voltage to the front and rear turn signal lamps through their respective control circuits.
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Did you check the RT STOP TRN fuse 15amp insturment panel fuse box.
Fuse Block - I/P
Left of the I/P behind the side trim panel
If the fuse is good , you could have a wiring problem or the BCM is bad .

Dear Alex,
The problem is in the bulb, or the socket, or the wiring to these.
Whenever a turn signal flashes fast, know that one of the bulbs is not working.
You have already identified the problem as being the front one. Problem could be the hot wire, or the ground wire, or the ground connection to this bulb.
Start by taking a tester to the hot wire, and see if it is receiving electrical impulses when the turn signal is on.
( It probably is, unless the car has been in a wreck and has been improperly repaired.)
Then check the socket or the wires to is and see if the bulb is grounded.
I suspect the ground is defective, and either a new socket or a repair to the ground wire should fix you rights up.
God bless your efforts.

take it to a body shop

sounds like the rear bulb is bad, check it if bad replace it if not replace the flasher canister.

You have a bad connection at the rear passenger side turn signal. It is either the connection is corroded or a wire is loose on the ground side of the circuit.

This may have more then one bulb in the front or possibly a bad socket try wiggling the new bulb in the socket to see if it will work.Compare all turn signal lights that come on the passenger side to those drivers side.Some vehicles also incorporate sidemarker lights with the turn signals.

Sounds like you need to replace the drivers brake/tail light.

Check for head light (daytime)relay to be bad,this might have to do with the turn signals also,if the turn signals on this car,also have running lights in them,If this relay is not bad,replace the body control module.

replace flasher......usually located in fuse block area...listen in this area....select passenger side ...then select driver side...you can hear flasher clicking...you have seperate flashers for each...FLASHERS are small cubes plugged into fuse block....probable bad driverside flasher