Is the Harry Potter part really split up between the two parks? Do you have to get a park hopper or two separate tickets to get to it? My husband bought us tickets but only to Universal. Didn't know Universal had two different parks at the time.

There is a Hogwarts part in one Park and the Diagon Alley part on the other. A park hopper ticket allows you to ride the train between the two, which is themed like the Hogwarts Express and is different in each direction. For the whole experience, you should have admission to both parks and the park hopper to ride the train

Yes you need tickets to both parks

Yes, part in islands of adventure and part at universal studios via the hogwarts express train.

Yes. You must have a park hopper to ride the Hogwarts train and visit the other part of Harry Potter World.