Kingma

1. No, not in all of them. The one's you do need to complete are wonderland, deep jungle, agrabah, atlantica, halloween town, neverland, and hollow bastion. The coliseum and Winnie the pooh-book are not necessary. I don't know about traverse town though..
2. Follow these three to the graveyard. Getting there, on your left there should be a floating iron plate with a candle under it that you can lit. Do that, then stand on it. You will be in another part of the graveyard. Go over that weird snake ground thing by activating it on the foot of it and then you will reach the bridge. Go over it, not under it. Then you will reach the house of oogie. When checking there you might find a green door. This won't open. Go to the top of the building into the small cabin. You will fight the three kids in there. When beaten them. Activate the machine that will open the green door. You will find oogie.
3. What do you mean.. The Hercules Cup? Just continue the game.
4. While defeating bosses, you will find some of Ansem Reports. You might find more if you do some extra things, like the book of Pooh, but I'm not sure.. Anyway, when Leon and the gang returned in hollow bastion they will be in the library at a moment. Talk with Aerith. She will give you a lot of Reports. Talk AGAIN with her, to get a surprise..
Good Luck!!!