Ok, to update the situation,
I took my car to where I had the rebuilt alternator installed, they ran a check and the alternator is fine, but only running at 51A out of the full 80A, thus, not charging the battery enough. He said the main belt's tension is too loose and that would cause slippage, the slippage would cause alternator to run at partial amperage, and that the slippage can also cause overheating since it runs the water pump as well...what do you all think? visual inspection of the belt appears chewed on one side slightly. Is it a major cost/job to replace the main belt?
Please Advise, thank you in advance, I really appreciate everyone trying to help