A: Yes, it’s a bit odd, but yes, that’s how it works. Although you’d have to assert its existence, i.e. play it, in order to claim that win. But if you have it in your hand you become eligible to play it when the game ends.

It is functionally similar to the Secret Cultist Surprise card in Cthulhu Fluxx (although, unlike the Secret Cultist, there’s no penalty for using/revealing it early). Since Chrono-games don’t have Surprises, there’s no standard framework to describe a card you can “play at any time directly after a specific play you’re reacting to (including a game-ending one)” but if you’re familiar with the Secret Cultist, that should be your frame of reference.

For those not familiar with the Secret Cultist, it is a Surprise card found only in Cthulhu Fluxx which says:
Out of turn: Reveal this card any time an Ungoal causes the game to end. You win!
During your turn: If you play this card, you are revealed as a secret cultist, and miss your next turn!