So Trump can just say, "I'm not President today"

[Bernardo de La Paz]

3. No, he is ALWAYS prezi. It's more fine-grained than that. He does not get to say when he is on "Official Duties",

Official Duties is the question. I think even the Supreme Court in its current membership would say accepting a bribe is not an Official Duty.

It is determined by context, because it needs to be more carefully delineated in law (Hint to Dems for when we regain power). But absent delineation, I would say that even in the Oval Office if he solicits a bribe it is not an Official Duty (hence is impeachable during term and prosecutable after term). He might be hosting a foreign leader and hence would nominally be on Duty, but that does not excuse a bribe, so whether you say that at that instant he is "On" or not, doesn't matter, in my book absent more definition by law or precedent.

He is prezi even while asleep or golfing or changing his diaper. A President is always available whether "On" or not, 24/7/365.