I'm not exactly sure what the problem is, but if the two are related, it's going to be a weird relation. The reason I say that is because the alternator should feed the entire electrical system, and when it is not the alternator light should come on and the battery should power the accessories as backup. I would also think that if the electrical system were to short out completely, that you would lose not only your transmission shifts and stereo, but also the spark from the ignition which would in turn kill the motor, causing the car to stall out. Since the car is an ATX, as soon as the motor died it would simply coast to a stop until you put it in neutral and restarted the motor with the key. At the very least the motor would get a weak spark and run rough, but if the electrical system is weakened completely the engine shouldn't simply run and accelerate smoothly as you describe.
This may be 3 seperate problems all occuring at once, but not knowing where to go with this one I can't say for sure what the problem might be. Best idea for now is to get the power steering leak fixed, either repair or replace the alternator and see if the problem persists. That's the only advice I can offer for now.
