Testing an '01 Alternator

I have had this Cherokee over 2 years and love it. Since I bought it, it has had an engine speed dependent whine (sounded like a tranny low on fluid). Dealer couldn't find anything; changed the serpentine belt and that helped. When I switch on the A/C or defroster, when it is cold, I get a chirpy belt. That stops after a bit. I started it the other day, very cold outside. Chirpy belt again with the defog. on. I noticed the voltmeter was at 9 and I had a check gauges light. Stopped, restarted and it was fine. In fact, it seemed to be charging higher than normal for a little while. This morning, same thing,. Voltmeter was between 9 and 14. Shut it off, but it didn't want to restart right away. It cranked a few times before it caught. Intermittent alternator with a sticking shaft or bad bearing? Any and all help is greatly appreciated.

When you say engine speed dependent whine are you hearing that directly off the engine or are you hearing the whine while the radio is on? If it's while the radio is on then you probably have some noise interference feeding into the wires. For the belt problem is it properly tensioned or could it be slipping causing the squealing? As far as when you turn the air on it sounds like you might have a problem with the a/c compressor bearings as well. For the power problem check all the cables under the hood make sure none of them are loose or corroded as that could cause problems with it charging as well, not sure if the 01's have it or not but also check the ground strap from the engine to the firewall make sure it's tight as well.