Air conditioner only works on one. when on two air conditioner light goes off!

Check for spark and fuel to the cylinders.
Could be a bad connection.

Below is a fuse box diagram for inside car and under hood. You said you have checked all fuses. If the fuse box diagram is correct it looks like you have fuses and relay under hood for interior lights and door locks.
https://fuse-box.info/mazda/mazda-protege-2000-2003-fuses
Just my thought, your amp drained battery, if you have no blown fuses could you have an open circuit. What have you done about the bad amp, could you have a problem with the repair made to amp. If you have a bad relay it could create a open circuit by contactor no functioning as it should.
I will tell you if the relay are the same I have swapped relay with another know good relay. Example My friends fuel pump was not working. His air conditioner was working, the relay were the same I swapped them and the fuel pump started working and air conditioner did not. We knew it was a bad relay.

I would check into your transmission at this point and eliminate that before moving on. To have a shop look at it and diagnose is only 80 bucks or so.

check ur switching box make sure is turning the ac off disconnect form the switching box inside and see if ac goes off if so control box is at fault repair or replace. Good Luck

MAZDA BRAVO B2600 B2500 1996 2009 WORKSHOP SERVICE MANUAL

This will surely solve your problem.I got mine solved too.

max towing capacity is 1.8 tonnes (1800klgs)
The towed should have electric brake control as the mazda has no traction qualities on the rear end under brakes.

make #1 piston at top dead center as to see where the distributor goes and lined up with. the rotor must line up to #1 spark plug. and the firing order is 1-3-4-2. the rotation is clockwise.

the blower motor has no affect on the AC system,
start the engine and turn on AC and watch the AC compressor to see if clutch engages,if it doesn't the system isn't full,if you are correct the clutch should be engaged and should quit when you change heater speeds,

Hey try out this link here, might be helpful.. 2005 Mazda Bravo B2500 Engine Torque Service Manual Download

With regards to the above problem, I have just recently experienced the exact same thing with a 98 Mazda Bravo b2500 (this is a diesel).The symptoms were after driving over some corrugated dirt roads the vehicle would not rev over 2000 rpm and at that point would blow heaps of white smoke and misfire, but would idle beautifully and rev smoothly up to the 2000 rpm. Also noticed when vehicle was cold it would drive good for about 5-10 mins then symptoms would start again.

Fuel filters were changed, sediment trap cleaned,different fuel tried and checked all lines and system for air entry, problem still persisted. While checking injector pump lift pump pressure I noticed that the pressure would drop right off at the 2000 rpm, maybe a lift pump problem?? After consulting the workshop manual I found there is a small stainless steel thimble filter under the injector pump fuel line input union bolt, held in place with a small spring. Pulled this out to have a look and it was full of crud, cleaned it all up and put back together and have a guess what......goes like a brand new truck!!

Cheers