I don't like the amount of corrosion on the positive side of the alternator. That cable could be internally compromised. Something is wrong in that circuit, and it is way possible to have 2 duds out of the box. Happened to a person a work.I don't know about the first question or how to find out. But, the alternator has a voltage regulator built into it.
I would be doing a continuity test on the wires and check all the grounds in the engine bay.