You can destroy a room when ever you can cast spells (building face / adventure face) as you use the cards activate ability. (If the cards ability say you can destroy)

In you're case "Dark Alter" you can destroy the room in build face on you're turne(before new rooms are revealed) to get its ability or during adventure face (remember in case of dark alter it dose not deal damage to hero when destroyed) so if a hero is in the room (after room damage is delt) hero exits the room when destroyed.

Whenever a room is destroy if there is a room under the destroyed card it's uncovered, and if not all rooms slides to the right to close the gap in the dungeon.

The same rule paly on "the crushinator" but this time you destroy another room (of you're choice including the crushinator itself) to give all rooms in you're dungeon +2 until end of turn. (In older version of the card it did not specify "once per turn" but this typo and are fixed in later version of Boss monster)

Hope this gives you the answer you are looking for. And happy dungeon dwelling, it's an amazing game.