I know one of the rules is to not work on the game before the jam starts, but is it ok to use pre-made assets?

For example, if I wrote a script for a past project and I find that it might be useful, is it cool to reuse it? What about artwork/audio/other non-code assets?

Also, what about third-party assets (like assets from the Unity asset store)?

You can use pre-made assets, however you can't import them into the new project. You'll have to rewrite any code you've made.