It's mentioned that '__attribute__' is allowed, does this cover the 'cleanup' attribute, supported by both clang and gcc? and about extensions, it's said "avoid using", is that a hard rule? what about extensions that are supported by many C compilers, ex. 'typeof'?

Honestly I'm thinking  or loosening the rule since its mostly unnecessary, It's fine to use attributes that don't change runtime behavior. I'd personally not use typeof but I made it not a strict requirement. 

I’m not super familiar with how game jams work. When the rules say “entries must be exclusive to the jam,” does that mean I can’t, for example, post my source code on GitHub or distribute them anywhere else?

Generally you can do whatever you want with it after the game jam, but the game must be developed during the game jam