A:
Perhaps.
If the question is whether a President may vote for herself, the answer is yes. (RONR p. 402.)
If the vote was by ballot, the president did not vote and the result was announced, she may not vote. (Parliamentary Law, p. 493.)
The president (and anyone else) may only vote before the polls are closed.
If no candidate receives a majority, the correct procedure is to re-ballot, unless the bylaws prescribe another method.