[DWar]

If at some point and for whatever reason ZERO is proven to be holding the office of the Presidency illegally, What happens to his appointments?

Those confirmed by the Senate like SCOTUS Justices Sonia Sotomayor and Elena Kagan; all cabinet secretaries; Homeland Security Director; etc.

AND those he appointed on his own during congressional recess or that he didn't need congressional approval for?

[Seizethecarp]

If Democrats can “persuade” Obama to resign (the more obscure the reason, the better), Biden becomes VP and all prior presidential actions will be locked in for the immediate future with no messy uncertainty resulting from subpoenas of BC’s or deposition testimony as to who vetted him as NBC.

If President Biden saw a criminal probe of any pre-inauguration actions by Obama, such as Chicago pay-to-play or hiding his Kenyan birth, in my non-lawyer estimation, a blanket pardon of Obama by Biden would likely derail any attempt to hold a trial at which evidence could be entered to prove Obama guilty or threaten to invalidate Obama’s presidency.

Having lived through the Nixon resignation, Ford's pardon to “spare the nation the trauma” from having a former president in the dock enraged the Democrats and perhaps cost Ford the 1996 election.

Biden would, of course, use a similar rationale here to avoid losing the African American base by invalidation Obama’s “transformative” presidency. Given Obama’s iconic negation of the US history of slavery (overlooking his Marxist Alinski persona) on balance a lot of citizens would accept leaving Obama’s eligibility uncontested.