If a monster is being spawned on ice (or some scythe traps, or pits), does it count as having entered the tile for purposes of having to roll? For example, if I freshly spawn a monster on ice, do I have to roll and if I roll a surge, I won't be able to activate it this turn?

I do not think so. You are already in that space when you activate. You haven't entered it as part of your move.

I agree. Even if you rolled for the ice immediately, ice only has the power to end your current turn, not any future turns, so since the monsters haven't been activated yet, it wouldn't do anything to them.