Thank you so much for answering!
As for changing repo visibility on Github - I wasn't able to do that as a student, that's good.
As for changing RC-project visibility - I was able to do that as a student, provided I uploaded my private Github repo as a RC-project on my personal student space, not through copying the public repo project on RC from the course workspace. RC asked for my student Github credentials and from there it was as if it was any other project.
(again, obviously if a student wants to cheat she will cheat but I wonder whether uploading private repos to RC should even be allowed, for this exact reason)