2 questions:

Let's suppose you reveal terminus (or any other miracle really) for your draw step and the 'you may cast this for its miracle cost' trigger goes on the stack. Does paper rules allow you to re-hide/shuffle it into your hand and brainstorm it back to your library, effectively bluffing that you still have it?

2nd question. Miracle trigger goes on the stack. Your opponent clique's you in response and puts terminus on the bottom. You draw a new terminus. Can you cast the new one for W? If q1 is okay and q2 isn't, what stops someone from triggering terminus 1, brainstorming it away, and then deciding to cast terminus 2 in their hand for W (I don't know why a player would ever do that, but for the sake of argument let's consider it)