'92 Mazda MX3 V6 5-speed 206,000 miles

Multiple issues with a fairly new car. I'll start with a little history: One owner for first 200,000 miles (kept and transferred a complete record of maintenance) who gave car to his son in perfect condition. It was driven for about 5500 miles and got in a front end mostly cosmetic accident. I bought it 5 months later (it may have been started once during that time) and it ran for 2 months. During this time, the 'charge batt' light would be on when I started the car and go off after 10-20 minutes. It would still come on at high RPM's (above 4k) even after running for 2 hours. I had it checked at the local parts store and both battery and alternator checked out good. Near the end of this two month period, the car started stalling after putting clutch in usually after coming off the highway. The frequency increased to the point that it would stall at most stops. Tack reads 500rpm, engine sputters, rpm's drop, it catches, goes up to 1000 then back to 500. It would eventually stall out if I dont give it some gas. This was not too bothersome until it stalled and would not restart on Saturday.

Earlier on Saturday I had it in to a reputable oil change shop. There is no release for the hood inside the car but I didnt get out to tell the techs until they had already disconnected a ground cable that connected to my fuse box under the dash (I found the wire on Sunday). It was that night, roughly 60 minutes total travel time when the car quit starting. It acted like I had blown a fuse on stopping (lights went out, radio died, presets reset). I took the key out and put it back in. Lights and radio came back, but not enough juice to start. The next day I checked all fuses inside and under the hood; all good. I jumped it and it started right up. I drove it to my house, let it idle for 20 minutes, drove it on a short trip to get the other car and it stalled on the way back. Battery wouldnt start the car and I jumped it again.

I took the car to the parts store again and they informed me after applying a load and the battery dropped to 1.2 volts that my battery was shot. I bought a new battery, installed it, and tried to start the car; no dice. I jumped the new battery and it started back up. Drove it, stalled, wouldnt restart. Took it back the the lube shop, had them reattach the ground wire, let it idle, tried to start, still not enough juice. Jumped it and it runs till it stalls, which is at every stop now.

So my question is two part:
1.) What is causing the stalling?
2.) Why wont the battery charge?

Other notes, I have read many of the questions and it appears it may be an issue with an Idle Air Control or an Idle Speed Motor. Where should I look for that? I was told by two people to start the engine and disconnect the positive batter terminal, which I did (not having read the many answers that said not to do this) and the car didnt stall. I have a multimeter and will check the voltage across the terminals, but if that checks out, what other cause could there be for the battery not charging?

I'm a novice at this but trying to save some money by doing the work myself. If anyone has information or an idea on where to start, I would appreciate the help.