inauguration day January 20
An incoming president of the United States becomes President at 12 noon on January 20 next following the election in November.
January
The New President Chooses a Replacement , (:
president Abraham Lincoln
The electoral ballots are officially counted at a joint session of the new Congress on January 3 following the election.
The electors are the people who actually elect the president. When the people vote for the president, they are actually choosing the electors who will cast the official votes for president.
The vice president would become president no selection is done by anyone
No. It is quite unlikely that this would ever happen. When the Vice President becomes President, a new Vice President is selected and becomes next in line. Only if the new President were to die before a new Vice President was selected would the Speaker of the House become President. Then a new Vice President and a new Speaker would be selected and they would both be ahead of the President Pro Tempore in the order of ascendence. The Secretary of State would become President only if the President, Vice President, Speaker, and President Pro Tempore all died at essentially the same time.
The Vice President, Joe Biden, is next in line for President.
If the VP dies first, the president would choose a new VP. If the president dies first,. the VP would become president and then would choose a new VP. If the president and VP both die at the same time, the Speaker of the House would become president and then he would choose a new VP.
The vice-president is promptly sworn in as President if the president dies. An new vice-president is then appointed by the new president subject to approval by Congress. However, it the president dies when there is no vice-president, the Speaker of the House of Representatives would become the president and if there is no House Speaker, the President Pro Tempore of the Senate would become president.
I don't believe there is a limit to the number of terms an individual can serve as vice president.