If Ms. Marvel perplexes Xavin's defense while he is on click 5 and Xavin goes back to click 1 at the end of the turn, does Xavin retain the +1?

I would say yes since he is neither damaged nor healed. Waiting for a confirmation.

I think clicking the dial counts as"healing" or "damage", so I would say no.

He would retain the modifier since it is not healing or damage.

I would agree that, since it is not said to be healing and it is not damage and is simply turning the dial, the perplex remains

There is a precedent set for turning as its own mechanic, above and beyond healing and damage (Oracle, Mister Immortal)

Correct, Beacuse he is not taking damage, nor is he healing, the modifyer remains.