Incorrect, the electoral college cast the elector votes which elected him. No matter how crooked the underlying popular election was, those elector votes are what legally matter.
Every state is going to be different, but I would say generally yes, because the law needs to recognize the reality that a stolen election is generally not worse than a civil war, so election integrity work needs to happen BEFORE the election is over.
As an example Romania had an election, then they identified what they considered to be irregularities, and the constitutional court decided to void the result. Now the whole country is in a very tense situation and foreign investment is running for the hills.
