Besides having a bad alternator, that I can't.

It's impossible to say for sure, but it's entirely possible all the problems are due to low system voltage. The many computers can't tolerate low voltage. Rebuilt generators aren't that expensive. I found one on rockauto. Com for less than the cost of one tank of gas. If you can't afford that to fix the car right, you can't afford to drive it either. There's no point in doing any other diagnostics until you have an obvious possible cause eliminated.

What do you want to replace yourself? You said the thermostat was removed and replaced. Was the old one put back in or a new one? What kind of "test" was done by driving the car without a thermostat? That's not a normal part of any diagnostics.

A lot of the cost of replacing the generator is the labor to get it out and back in. That may be much more difficult if the vehicle isn't on a hoist. Before that is done there are some tests that should be done to eliminate other potential causes. It would be a shame to go through all the work of replacing the generator only to find out the new one also doesn't work. If all the voltages are present, it's possible only the voltage regulator or the brushes are bad. That assembly can be replaced separately but it costs a lot more than an entire rebuilt generator. You would still have to remove and replace the generator plus disassemble it to replace the part.

You have multiple cooling system problems but haven't listed any test results.

"I was getting hot air from heater but the hot/cold temperarture guage wasn't working"

What does "wasn't working" mean? It stayed on "cold"? It stayed on "hot"? It bounced around? Is that before or after the mechanic replaced the thermostat? If it's after, the new thermostat may just be missing a bleed hole. That can be drilled into it. A leaking head gasket can cause air to pool under the thermostat so it won't open at the right time. They only open in response to hot liquid, not hot air.

The fluctuating temperature could also be caused by improper operation of the radiator cooling fan. That could be due to a computer not working properly and that could be due to the charging system not working properly. Jumping in and replacing a bunch of random parts just because you are able to is the least effective and most costly way to diagnose a problem. If you are going to pursue that route, start with a rebuilt generator, then see which problems are still there.