The driver's side fan is indeed the cooling fan. The PCM should start the cooling fan at about 205*F. There is a coolant temperature sensor above the bell housing, at the back of the engine.
Yes, both fans should run with the compressor on.
Jumper in TEN and GND, both fans should run when the key is on and the accelerator pedal is depressed. When I am working by myself, I use a shortened broom stick jammed between the pedal and the seat to hold the pedal down.
The cooling fan motor should have about a 6 amp draw. I cannot find the amperage draw for the condenser motor. Is the thermo switch you are talking about the one off the back of the engine?
I just replaced both of my fans. My cooling fan had only a 3 amp draw. And it would only run intermittently. I think there was a dead spot in the motor that would not allow it to start if the fan stopped on the spot. Since I was replacing the cooling fan on my 125,000 mile car, I decided to replace the condenser fan at the same time.