There's some conflicting information on the Michael Jackson thing.
This video covers the topic in great detail.
Cliff Notes:
Michael Jackson was 100% involved in composing music for Sonic 3
Sega maintains that they decided to remove his compositions entirely from the game because of the molestation scandal.
However, frequent MJ collaborator Brad Buxer (who is credited in Sonic 3) said if MJ was not credited in the game it was because he felt the Genesis' sound system was too weak to properly portray his music. At the same time, he also said he never personally played Sonic 3 and had no idea if any of Jackson's compositions actually made it into the game.
Someone who worked directly in the development in the game but chooses to remain anonymous said that MJ bowed out of composing music for the game about halfway through because he felt the sound system was too weak (confirming Buxer's version) and asked to not be credited. Now, the story goes, the whole development team was down about MJ quitting but some time later when the scandal hit they were like '

dodged a bullet with that one.' but the music MJ composed was kept in the game, unaltered. Now, as for what exact stages he worked on, that can't be 100% confirmed although the source said MJ for sure did Carnival Night. He also said MJ submitted Black or White to be in the game but it was removed due to opposition from MJ's lawyers. Sega should still be in possession of the unused FM sound source.
There's some legal issues going on with this stuff as well. So, we're unlikely to get more concrete answers than this.
Speaking of Brad Buxer, he was the keyboardist for the band The Jetzons and in 1982 they released this song
This isn't isn't a stretch. That song is just flat out the song used for Ice Cap Zone. Lazy b*stard didn't even come up with a new beat