2. The Quarantine can ask questions about the past at the beginning of each session. The MC answers questions on a hit, but on a miss, the player answers instead. Why? Specifically, why is that the miss option?
Look at the questions list! If you're a player, what questions do you want to ask? If you're the MC, what questions do you want to ask?
The MC answers/player answers framework works because of the different questions. When a player gets answers, he gets to know what the Apocalypse is like, what it's causes and effects are. When a MC gets answers, he gets to know just how nasty and destructive the Apocalypse was.
So the mechanic alone seems odd somewhat (did to me, too), but if you take the list of questions into account, it is not different from any other AW move (i.e., on a miss, the MC gets to make a move).