I want to disconnect my alarm system from the ignition??

Disarming an Armed System/Silencing an Alarm
If system arming has been requested by the keyless entry transmitter, it must be disarmed.
Important: Using the power door unlock switch or manually unlocking the doors does not disable the CTD armed mode. Also, disconnecting the battery or pulling fuses does not disable the armed mode, since the BCM stores the CTD mode status in memory.
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To disarm the CTD system in arm pending mode, SECURITY indicator flashing and doors open, perform 1 of the following:

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Press the UNLOCK button on the keyless entry transmitter.

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Insert a valid key into the ignition and start the vehicle.

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To disarm the CTD system in the armed mode:

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Press the UNLOCK button on the keyless entry transmitter.

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Insert a valid key into the ignition and start the vehicle.

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To disarm the CTD system when activated, alarming mode.

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Press the UNLOCK button on the keyless entry transmitter.

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Insert a valid key into the ignition and start the vehicle.

Plug your ears first, open the car with key, open the bonnet to get to the battery, disconnect one battery terminal and cover this with rag to avoid a short circuit. That should reset everything - alarm, radio. Do not lock the car. After an hour reconnect the battery. Hopefully alarm will have reset and then use the key in the ignition. Hopefully starts but you should buy a replacement button for your car and security system. If alarm sound again, disconnect battery again and call an auto electrician.

that's a mechanical, not electronic issue. there is a micro switch which rests on the ignition lock cylinder which has failed. I'm not sure that it would be a simple matter of disconnecting it because you might need a while just to get to the circuit. and that circuit is not monitored by the alarm or computer.

The alarm system somehow got activated , this is usually because the battery becomes discharged or disconnected try doing this:
Remove the key from the ignition
disconnect the negative battery terminal
put the key back in and turn to ON
exit the truck and leave door open
reconnect the battery terminal
get in and leave door open, if the alarm horn stays off it should start.

First, Have your Battery tested. The Alarm systems in Ford made Products are very sensitive to Voltage. There are 3 systems in the car which interrupt power, the Alarm system (horn honking) and the Battery saver and finally the starter interlock system.

The Alarm system will do several things to disable the car from starting. It will reduce the voltage to the starter to prevent the engine from turning over. Some will even kill the ignition system so that if the starter is jumped, the car still won't start.

The Battery saver will disconnect any system to prevent discharge below a minimum threshold. Unfortunately, when the Alternator is working extra hard to charge a really bad battery: it will disconnect the charging circuit because it reads the Draw going to the Alternator to produce the power as a parasitic drain. Even at 70mph I have seen the charging disconnected and the vehicle coast to a stop when the electric runs out.

The last system worth mentioning is the Starter interlock. Under the dash and at the top of the Brake pedal lever is a switch. When you press the brake pedal, the switch allows the starter to crank provided the shifter is not in D or R. Drivers feet routinely hit this switch and either move it or break it. When it breaks it can short and drain the battery.

As you mentioned a Random problem, the Brake switch can shake to create a random problem if it is loose or broken. Your rear brake lights can be affected.

With the horn honking, at least part of your problem is the Alarm system. You can have a bad ignition switch too, which reads the keychip to disable the alarm. Your keychip may be bad and setting off the Alarm.

I had a new Lincoln myself which set off the Alarm randomly. I actually slept inside the car one night so I could turn off the alarm in the Apartment complex parking lot. Did'nt know if it would start again if the battery was disconnected and then reconnected. The Battery was shorted with less than 1000 miles on the car. It was a factory defective battery less than 3 months old.

But your car has many years and miles on it so it was worth mentioning the wear items. I hope my solution is helpful.

the system is either hooked to the battery or it has a fuse try disconnecting them

The 'Keyless Entry & Burglar Alarm System" is activated. You must 'Disarm' the system using the Keyless Entry Remove (Key Fob) to "Reset" the system. The reason the engine won't start is due to the burglar alarm - it has a "Starter Kill" circuit which is activated when the alarm is activated. The alarm must be DEactivated to DEactivate the 'Starter Kill' circuit.
Another way to start the engine is to get in the car, put the key in the ignition and turn it to 'ON" and wait 3 to 5 minutes until the emergency flashers stop/turn off. Afterward, you should be able to start the engine. NOTE: This does NOT reset the burglar alarm. It will go off again when you enter the vehicle without using the remote/key fob.

last ditch effort , disconnect the battery and wait 10 minutes and hope your system re sets itself , not knowing what make your car is , makes this hard to answer, or if it was a factory alarm or aftermarket ,,,, If its a factory alarm, you can do this Open the door with the key. (the alarm will sound but ignore that)
Close the doors, put the key in the ignition
Turn everything off that takes power when you got the ignition on.
Turn the key into first position (IIRC) the alarm will go off again, but still ignore that.
Then sit back and relax for exactly 15minutes, without touching anything nor opening any doors.
Then turn off the ignition.
That's it. Your alarm is now disabled.
Start the car and enjoy.

disconnect the alarm system from under the dash.battery to starter direct will turn the engine over fine but ignition system still runs through your alarm system.It's also a theft prevent system so your car will not be stolen.The alarm went bad preventing your car from starting.That means putting the ignition wiring back to factory.