For your first question: that should be fine as long as you can finish them within the time frame! That's very thoughtful of you. (But if you can't finish them within the time frame, we'd rather you submit one finished game than two unfinished ones.)
For your second: This is what "exquisite corpse" is: https://www.tate.org.uk/art/art-terms/c/cadavre-exquis-exquisite-corpse#:~:text=.... It involves drawing the next part of the picture while keeping the already drawn parts intact. So that's how we want you to approach it: think of it as building on top of what's already there, rather than knocking it all down and starting over.
We have in mind a more fleshed out version of the game. Have you ever played a game, or watched a TV show where it has so much potential but squanders the execution at every turn, and you just KNOW you could do it better? It's sort of like that. By "build upon the framework", we mean you should keep the bare bones of the story intact. So, if the original story is "A guy went to the store and bought a lightbulb. The end.", your new story should still involve a guy going to the store and buying a lightbulb. If you take that out, it's not recognizable as the same story anymore. That's where I would draw the line for too much change: it's missing the bare bones and might as well be a totally new game.
This isn't a hard rule because it doesn't work for all games. Personally, I've noticed that with some entries, the badness serves the narrative or the point it's trying to make. I don't know how those can be fixed without turning them into completely different games, so you might need to do a sequel or something else entirely!