AC Compressor/Power Steering/Battery Light

Hi Guys. I recently received a car from my parents. A 96 Mercury Sable. It was skipping shifting from first to second gear. And after a little more driving It was skipping hard coming down. It also developed a loud sound coming from the belt and pulleys on the left under the hood. Which I took to mean a loose belt or bad pulley somewhere down the line. As a man with limited resources, I took it in to get the transmission looked at. Turns out I had a leak and was low on fluid. They changed the fluid and fixed the leak, and told me that my AC compressor pulley was loose, and it was a matter of time. So I was like cool, I'll take it home, and let it sit until I have the funds to get it fixed. (This was a transmission only shop, but the most trusted in town). On the way home I heard the belt squeal and a burning sound, and then a little snap that I knew was the belt, luckily I was at the top of a hill. I lost power steering, and my battery light came on. I managed to get it to in front of my house, the engine stayed strong, which let me get it turned around. When I stopped I noticed I was hot. Not redline, but about 3/4 of the way towards the H. My redline being a few notches above the H.

My question to you is, Does the same belt that runs along the AC compressor pulley run along the power steering pump and alternator, and what are the chances that I screwed something else up by letting the belt snap.

Yes it does, and your likely fine. Replace the component that failed and the belt and see what happens.

Yes, It has a serpentine belt. It runs everything. The worst thing that could happen is the engine get too hot. Sounds like you lucked out, 3/4 hot shouldn't be hot enough to cause damage.