Yes, a former judge could run for president. I am not sure that a judge would even have to resign before running, but maybe so. I can not think of a judge who has been considered as a presidential candidate or that the question has come up.
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He did not resign, but he declined to accept a 3rd term as President
Yes but only after winning the presidential-vice presidential election, the Governor would have to resign his position prior to taking office as VP.
A vice-president does not have to resign his office in order to run for President. Martin Van Buren, Richard Nixon, Hubert Humphrey, George H. W. Bush and Al Gore all ran for President while holding the office of vice-president.
Practically, no. Since the vice president is made president if the president is incapable of performing his duties, they would be constitutionally unable to fulfill the obligation if the president were to resign or take ill.
President Nixon.