The thing under your alternator is called the air conditioner compressor.
The screeching belt, I would suggest one of two things. One, loosen the belt and try to turn the compressor pulley by hand. If not, replace your pulley / compressor. Not sure how they come apart.
Two, if you can turn by hand, then you should check your refrigerant level. There is a plug on the frig line near the passenger front engine compartment. Pull this and put a jumper wire. If the compressor kicks on, add refrigerant. If not, you got issues elsewhere.
Timothy
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