Would a diff/patch be DMCA-proof then? Or would it fall under derivative works?

I'm guessing it is more likely that these repositories were searched for by staff/professors than fully specific code was searched for.

I don't think you can claim that changing code absolves you of copyright issues, it might make it harder to find though.

APIs shouldn't be copyrightable as they're necessary for interfacing. The solution to a homework problem shouldn't be a derivative work of the problem, and so it should be possible to distribute the solution in a way that doesn't infringe on the university's copyright.