Of course he is.
No person shall be elected to the office of the President more than twice.
There are other ways to become President (other than by election), one of which is by succession.
Of course he is.
No person shall be elected to the office of the President more than twice.
"no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
Bottom line: it would be constitutionally questioned and decided by the courts.