Nope. Those are all transformative works and are fair use. The remix, cover, or fanfic are all considered new works as far as copyright is concerned and the writer of them can do whatever they want with them including sell them. People get their fanfics published all the time they just usually don't sell well. People make covers of songs and sell them all the time. I can think of several youtube channels that only do exactly that. Anyone can just go record themselves playing Wonderwall and try to sell it because them playing that song is a unique work. I think trademarked stuff is more restricted on what you can do with it but I'm not sure on that.

AI is also even more limited in regards to transformative works than humans because you can't copyright the direct output of an AI. So if, for example, you made an AI output a cover of a song you could still do whatever you want with it but you couldn't own the rights to it. Anyone else could also take it and profit off of it. The only way to copyright AI output is to create a transformative work based on that output. You can use the AI output to create a new work but you can't just call the AI output your work. In my opinion that's exactly where the law should be. You can use AI as a creative tool but you can't just have one generate every possible picture of something and copyright them all.