A: Yes, that’s exactly what she can do. The Secret Cultist, is, naturally, working for the downfall of everyone, staying hidden until the Old Ones rise to take control, at which point the Secret Cultist comes out of hiding and claim at least enough credit so as not to get destroyed. Being a Surprise card, it’s meant to be played out of turn, including, in this case, specifically just after the game has “ended” due to an UnGoal.
Sorry to break it to you… Thanks for playing our games. Maybe she can put in a good word for you after the apocalypse or something.