Welcome to another Arizona Fieroite.
When you are running the AC, get out of the car, open the rear deck, and listen. You should hear a click and the engine will slow down momentarily. This is the AC clutch kicking in. Also, try the AC controls in Max, Norm, and Defrost with the slider knob set to full cold. Open your front hood. Does the radiator fan start when you turn the AC on?
Does the whining sound start when you turn the key to run (without trying to start it)? If so, that is your fuel pump. If it is loud enough to hear with the engine running, there is something wrong.
I'd need more information on the cutting out. What engine and transmission do you have? Has the fuel filter been changed recently? Are there any ECM trouble codes (Check Engine Light)? Does the engine exhibit any other problems? What happens if you accelerate slowly?