LEARNING CENTER

Pass. When partner preempts, a new suit is forcing. While 2 might be a better contract than 2, you can't play there. Trust partner's preempt. 

3. Yes, you have "only" 13 points, but your points are all in aces and kings so you shouldn't jump to game. Going to 4 would show the worst type of hand, following the principle of fast arrival. A typical jump to 4 would look like this: 

 QJ873  
 987  
 KJ3  
 KQ
 

4. You have a fit with partner and enough points for game, but you want to deny any slam interest. Jumping to 4 is weaker in this case than bidding 3. If you had a truly awful hand (0 points and no good shape), you could use a tool called a second negative. 

2 (Transfer). Yes, even with only 2 points, you want to transfer. This is a great way to get out of a potentially disastrous 1NT contract since your hand is likely worthless in 1NT and you might take a couple of tricks in 2. Transfers can be made with 0 points. I recommend always (100%) transfering out of 1NT with a bad hand and a 5-card major. 

4NT. First things first: pass is out of the question. Partner is not making a "sign off". Partner is showing a big hand (19-21 total points) with four-card spade support. You should be headed for slam. Keycard is used to double check that we're not missing two keycards and here, it might help if we want to find 7 or 7NT. Imagine partner with: 

 K1043  
 A8  
 AQJ32  
 A5
 

and 7NT has 15 quick tricks (although we have to be lucky if spades are 3-0). That said, partner has to be perfect for the 7-level to be right. Partner might also have a nightmare hand missing 2 keycards, which means you might want to stop at the 5-level which you can find out with keycard.

That nightmare scenario is also unlikely, so just guessing 6 is reasonable, but inferior. 

1. Partner has made a takeout double, showing an opening hand (or so) in values and three cards in the unbid suits (or 18+). East's 1 bid means that we are off the hook--we don't have to bid if we have nothing to say, but here we have a lovely spade suit that partner has at least three cards in. We should bid 1 to show partner that we have spades (this only promises four of them) and at least a little bit of life. Double here would NOT show spades.

It's easy to confuse a double by advancer with a double by responder on the auction 1 (1) Dbl, which would be a negative double. This is a very different situation since we are advancing after a takeout double. Double here would generally show values (and usually hearts). 1 promises 4 or more.