One person simultaneously prez and veep

[J. J.]

The President and Vice President cannot be from the same state.

That is NOT accurate.  The electors cannot vote for more than one candidate from the same state as the electors: 

Article XII

The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves ... .

There is the doctrine of separation of powers which would prohibit one person from serving in more than one branch of the Federal Government at the same time.

[J. J.]

Yeh, and it's really freaky phrasing as well.  It was Gerald Ford's excuse (misstating it) for joining the ticket in 1980, even though:

1.  He could have moved back to MI.

2.  Even if he hadn't and the CA electors had voted for someone else (Bush, for example), Ford still would have had enough to win.

[J. J.]

Yeh, and it's really freaky phrasing as well.  It was Gerald Ford's excuse (misstating it) for joining the ticket in 1980, even though:

1.  He could have moved back to MI.

Dick Cheney lived in Texas until he was named Bush's running mate, at which point he changed his registration to his Wyoming ranch.

Exactly.  It would have made a difference in that election, but in a few others, like 1980, it would not have.

[J. J.]

There is a school of thought that the original framers of the Constitution did not intend the Vice President to actually become President upon the death of the President. Instead, they intended the Vice President to assume the duties of the President but to remain Vice President. So yes, someone could be both President and Vice President at the same time.

Is this a historical fact, or just a school of thought?

I'm not certain, but before the 12th Amendment, every Elector had two votes.  The could cast both for one candidate.