How did Pope Alexander VI contribute to the French invasions of Italy?

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.