SonicDoom, it sounds like you already have mod ideas—three in fact.
Cave Story 2 has already been done at least once or twice. That's not to say that you can't try your own hand at it and come up with something different, but it's not the most original of ideas. Also, story-based mods have the challenge of syncing up (or not) with the original story. If you're interested in putting together an interesting storyline, it might be best to do something new that doesn't have to do with the original CS story.
That being said, I don't know what you might have in mind for a "Paranorman" or "Adventure Time" mod. I think I saw a commercial for something called "Paranorman" while I was watching the Olympics last week, but I don't know anything about it so I imagine that you could do just about whatever you want with those ideas.
I may be wrong about this, but I expect you would need a completely new game engine to make an FPS based on CS. Actually, from what I remember, I think people have done CS-like things in Team Fortress 2.
Also, I expect the pet idea would require massive assembly hacking. Maybe I'm wrong, though.