I have a 1996 Corolla (AE110) and when the car starts the headlights come on with the light switch off. They go off after a few minutes. How can I fix this?

check to see if the headlights can be turned on, if they are bright its not the battery. check the starter motor and the ignition switch and always check for loose and dirty battery terminals.

if you can get the valve pack replace it if not run new brake lines and remove the valve pack and add in a adjustable puportioning valve

It requires special tools and training to diagnose the ABS system. It is not something that really can be done at home.

What part doe sthe relay operate. ae110 means nothing to us with diagrams and we have none.

I would start with a tune up - plugs, wires, all filters & fluids changed. Make sure your tire pressures are up (check with a tire pressure gauge)

can you please explain what you are trying to do ,as quite a few typing errors are evident here

Please DO NOT drive in with the vehicle in this condition!!!!
What you have going on is that the brake caliper (part that holds your brake pads) is bad and sticking. Just remove it, get a NEW one from any chain autoparts store,and replace it. You will have to get a new set of pads as well,as due to the binding, the ones on there now are trashed.

Again,PLEASE do NOT drive in this condition as yours and your fellow drivers ,as well as your passengers safety is at stake.

Check your computer box. There may be a problem with it. Repair or change it.

try adjusting the thermostat of the A/C , that is one of the main reason of the change of condition...
reply if it will do the same thing

Bad ignition coil. Borrow a known good distributor to swap with yours, and if the problem goes away you'll know that's what it was. The ignition coil is inside the distributor body and can be easily replaced.