Retraction. The answer to part 2 is once. You only need to hit the ball once to win a set. This is the explanation (BTW, I thought 12 too):
Imagine if every time you serve you swing at the ball and miss. This is a fault. Do this twice in a row and you lose the point. Do it eight times in a row and you lose the game.
Now imagine you do this for your six service games and that your opponent also double faults on every serve. The score after 12 games will be 6-6 and the set will enter the tiebreak.
If you continue to swing at the ball and miss, and your opponent double faults, neither of you will be able to win the tie-break. But depending on who serves first you will either get to 6-5, or 7-6 ahead. When you you do, ace that serve and you will have won the set with your racket hitting the ball only once.