A: Double Draw is a Surprise found only in the More Surprises pack (so far!) To review, the during-your-turn instructions for Double Draw say: Draw again the number of cards you are required to draw during your turn.
This means whatever the current Draw rules are – right now, not whatever you drew at the beginning of your turn – plus any extras or bonuses granted by Rules or Keepers, that you currently qualify for.
Note that some such Bonuses say they can be taken “once per turn” and others stipulate a single time during the turn which they can be taken (“at the start of your turn, draw 2 extra cards”). If you have Keepers which grant you an extra Draw for having them in play, you get those.