If I draw the number of cards I have left in my hand to play, do I have to play them all? Which one takes precedence? Play All, or Swap Plays?

A: Once you have exercised your option to Swap Plays for Draws, you have no more plays left (you have swapped all your remaining plays) so your turn is over. So, no, you don’t play those new cards drawn. In that sense Swap Plays “takes precedence” since you may still have cards in your hand at the end of your turn even though Play All is in effect.

Specific example:
The Swap Plays For Draws card explicitly states that when this rule is in effect, you may choose at any time to play no more cards, and draw the number of cards as you have plays left. Play All says to play all your cards this turn.

So lets say you have five cards in hand. You play two cards, and decide you want to swap the rest of your plays for draws. Since you have three cards remaining, and Play All is in effect, you have three plays left to swap, so you draw three cards, thereby ending your turn.

Likewise, if Play All But 1 is in effect, then as long as you have more than 1 card remaining in your hand (which would mean you have plays left to swap) you would get to draw the number of cards in your hand minus 1, since the number of plays you have remaining is simply 1 less than the number of cards in your hand. As with Play All, of course, once you choose to swap your remaining plays for draws, you have no more plays.