Re: 101 - all good questions!
My own belief is that a criminal conviction is not necessary for someone to be disqualified from holding public office. But as you point out there are so many other questions.
A good but long paper is here:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3749407
I agree with you - narrowly crafted ruling so as to get as many Justices on board as possible.
In 2012 there was serving felon - WV native in a Texas prison who ran in the Rat presidential primary. He did quite well up again Zero.