I have code of the basic movement and interaction stuff that I've been using in my game and other jams that have been pitching and fixing to make it as good as possible are allowed on this game jam or not. Or do we need to make a new one on the game jam?

Strictly, we can't police this, but we encourage starting from scratch in the spirit of the jam. So long as the majority of the game is made during the jam, you'll be fine.