What causes the alternator not to charge in a 92 Buick Skylark?
If it's properly connected, it's just worn-out. When you get it replaced, make sure you get a new one and not a rebuilt alternator. I had a brand new Bosch alternator put in my 1995 Skylark about 4 years ago and it's worked like a charm ever since.
How hot is normal for a new alternator to get when idling for an hour after replacing it and the battery on a 1993 Buick Skylark?
They will run somewhat hot while charging; if you put your battery in discharged however, that makes the alternator work much harder. A alternators job is to maintain the charge in a battery not to charge a discharged battery.Keep a eye on it, it will probably be OK once the the battery is topped off.