Issues in self-publishing old work. Recommendations for Necromancy?
This is in response to Question 1:

The university only cares if some portion of your work is monetizable, i.e. leads to a product that people pay money for.  If not, they would prefer you to publish rather than not; it can only help them.

The real issue is your advisor and collaborators, if any.  They may have a claim on that work.  Before publication you should contact them and discuss possible coauthorship.  Resolve this issue before investing any more of your time; see other posts here for what happens when authorship is not clearly agreed among all participants.