First, please note that I had to edit your question as we are not allowed to answer multiple questions all at once.
Pope Alexander VI was only tangentially involved in the first French invasion of Italy that happened in 1494. One reason why the French invaded Italy was because Cardinal Giuliano della Rovere had a grudge against Alexander. He helped to persuade King Charles VII of France to invade. But this was not by any means the only reason for this invasion.
Alexander had more to do with a second invasion of Italy, this one happening in 1499. In that episode, Alexander agreed not to resist the French invasion. He did so in exchange for the French king's promise to help Alexander's son Cesare Borgia in Cesare's attempts to conquer Romagna. In this way, he made it easier for the French to invade Italy.