Is it “legal” for a Senior Vice President and Provost of a College to be Intimate with a PHD Candidate While working on their dissertation of the same School?
The law varies widely, but I doubt that there are many places that would have laws against this. But university regulations are a different matter. More, but not all, would have rules, usually to forbid it. It would be, in most of those cases, a violation of the VP, not the student, I think.
But the situation can be fine, provided that the VP has no influence whatever over he grading/ranking/prospects of the student. This might be the case or not. It would probably be unethical if the student's future depends in any way on actions of the VP, rules or not.
Whether it is wise is another matter. Reputation is important.
This depends on the rules of the university in question (and maybe also on the laws of the country). I've seen universities where relationsships between professors and students are fine and some where they create huge problems. At the very least, one should consider that - like in every company - relations between a "high" and a "low" person (in terms of their position) will probably create problems with collegues who might fear that this student will be treated better/believe the student is incompetent and gets only forward because of sleeping with the higher person etc.