When driving very slowly, like in parking lots, the power steering will get stiff when I make a turn, like pulling into a space, or when parallel parking where I need to turn the wheels while the car is stopped. The engine will shudder and almost stall. Then the engine management system (or whatever it is) will give the car a bunch of gas to prevent the stall and I'll lurch forward. Is this normal? I can't imagine a 3.8L V6 doesn't have enough power to operate the power steering at low speeds.

No that'* normal. I never have problem turning my wheels with the car on. Even pulling out of the driveway it turns very very smoothly.

You will want to check your throttle body and clean it and the sensors on it, IAC and MAF. Be careful cleaning the MAF, do not touch the wire.

This sounds wierd, but get your alternator checked. If it is on its way out, it can cause your car to stall like that. Worth checking

The car never actually stalls but it wants to, and it'* worse when I use the brakes and turn at the same time. I've totally gone through the ignition system (coils, plugs, wires) so I'm fairly sure it'* not that. As far as the alternator goes, my battery is charging very well, I've never had an issue with a low battery or anything related. I've checked the MAF wires and they seem perfect, but I'm not sure what to do about the IAC? Also how would I "clean" the throttle body, just with a rag or something?

If it gets worse when you use the brakes I would take a look at the vacuum line that goes to the brake boost and look for cracks. Have you checked your power steering fluid level?

There is fluid under the power steering cap, but I don't know if it'* full or not, there doesn't seem to be any kind of indicator. All the vacuum lines seem to be in good shape but I don't know for sure, I'll have to give them a thorough check when its not raining.

Could something wrong with the brake booster cause the ABS light to come on? Ever since I've had this car the ABS light has been on and this stalling thing has been going on. I've also always noticed that the brake pedal doesn't spring back immediately when I release it.

About the only time I get something like that is when I hit the stop. Car doesn't seem to like being on the steering stops.

I would say there might be a connection, hopefully some one chimes in because I am not 100% sure as to what though. . .