Bought my first 88 Audi 90-Quattro. A few questions from a mechanical newbie
 

Hey everyone, I just recently purchased a 1988 Audi 90-Quattro and since have stumbled upon some mechanical issues.
First things first,
1. I was driving home the other night when both of my headlights randomly flickered and went out. I then turned on my brights (since they really weren't too bright) and drove the rest of the way home. I used these to drive at night for a few days until the same thing happened to them. Anybody know what the issue is?

2. The guy I bought it from took out the air conditioning. I was looking at the engine with my gf's dad the other day when he pointed out that both the ac pump and belt were still in there and could be detracting from the power of the car. It's making a light screeching noise. Does this make sense?

3. At random times I will hear a loud screeching from the engine and then the stereo in the car will randomly shut off. Sometimes it's when I turn a corner. What is going on?

Any help would be very, very appreciated since I am far from being a wrench head.