Can I use an existing system to write a hack for the game jam? Is that allowable if the core game rules are listed in another product? Can I do that for a system I wrote?

And what format does the submission have to be in? Is an HTML rulebook permissable?

Thanks! I have never done a game jam before but I love this theme.

You can create content for existing systems if you like. And any format you prefer is fine. Most people who are making ttrpgs submit PDFs but whatever you got is great!