Of course the seller knew of the problems already. But it doesn’t matter. It (and they) is/are yours now.
The alternator’s only relationship to the current problems is that they’re both the same age.
Your choices are to have the problems diagnosed and repaired, to sell the car, or to junk it and take the loss as the cost of an education. But before you make any decisions, or lose any more sleep, get the diagnosis. Without it you cannot make any decision at all.