Github is a way to store your code. You should have one copy of your code in a local git repository and you should push that code up to Github at least once at the end of the jam. Experienced users push their code up much more often - basically every time they make any serious changes.
As for the tools for making a game, you can start with the list at the bottom of the announcement for this jam. https://itch.io/jam/game-off-2024#:~:text=New%20to%20game%20development%3F