Issues in self-publishing old work. Recommendations for Necromancy? Main Issue:  What credit should be given (and how should it be given) to the alma mater in publicizing old work?

Background: I entered and left a Ph.D. program in another millenium.  During this time
I produced some results, one group of which was to become my dissertation.  (At one point, my advisor said the equivalent of "you have enough to graduate; write it up".)  However, all that I did distribute during my time as a graduate student was a couple of preprints, one of which later got cited in work of others.  I did not finish the dissertation and did not get the degree (although I did get to attend commencement and walk across the stage).  If it matters, during the time I produced results I got one TA (teaching) grant, and no other funding.

I am considering self-publishing material related to the work I did in grad school.
I have already given presentations on some of the work;  I now plan to submit to ArXiv some of my work done while I was in graduate school; later I may follow up with results based
on this work. 

Question 1.  What kind of issues might I encounter in doing so?  Would the University have some recourse to discourage me?

Question 2.  If there are no intellectual property issues involved, what is an acceptable format?  (I was thinking: write a wrapper giving a brief history and introduction, insert my preprint verbatim, and close with acknowledgments and some follow up.  The preprint I distributed does not contain my dissertation, but is a key piece of it.  What would the
acknowledgment section look like?)

Question 3.  If I decide I also want to go back and finish
my degree at that program, (ideally by finishing the remaining requirement of submitting
the finished and approved dissertation, however unlikely that may be), would doing this
self-publishing be contraindicated?  If so, why?
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.