Hi, I would like to participate in this jam but not crazy about sharing my source code. Can I just publicly publish the binary on my entry's github page from a private repo? Or is that against the spirit / rules here?

can we be a team to create a game 

It has to be a public repository with the entire source code being public. But how you license the repo is your business

Considering this is a Github game jam, I think they are pushing to have public repositories.

Can always go private after Jam is over :)