Welcome Aboard!
1. I've been playing this game for twelve years and I still don't know the answer to that one. I would think that the higher the better, but I can't prove it. I try to have it as high as I can, just in case.
2. Just the three, if you have Fatigue turned off. Otherwise I try to have enough for a full rotation, i.e. six.
3. Nothing keeps you from doing whatever you want in your game. While I qualify all Petty Officers before anything else, because the qual is what makes a PO a PO. Promotions I try to leave for when the game recommends one. I do know promotions in real life don't happen all the time, and I try to play in a fashion that feels realistic to me.
The bottom line is that it's your game to play the way you want.