An engine usually has a higher idle speed when the ac is running. If the high speed idle does not operate then the ac will cause the engine to stall.
AC runs on the battery. If the car is off and you run the AC, then start the car, it will stall.
A seized AC compressor will tear up the belt... if it's a serpentine belt, or a belt which runs any other components necessary to the car's operation, that'll eventually cause it to shut down.
Indirectly it does. Gasoline powers the engine which powers the AC. Without the engine running the AC doesn't work. Also on many cars the AC will cause the cars gas mileage to be lower if it is running at maximum AC.
Idle could possibly be too low.
no
It could, the computer will disengage the ac compressor if the engine temp is too high.
if your ac is running and if you have a bad 02 sencor most likely it will not kill your car it depends on your sensor
yes
The AC pump is bad. When the AC is turned on the pump tries to turn, because it is bad the extra strain on the motor causes it to stall. Be carely this can break or through a belt. In short its like putting a "brake" on your motor.
You may smell coolant when the ac is running but a leak in the heater core won't cause the ac not to work.
AC Compressor
A little, the ac pump will put a draw on the engine more than without the ac on.