Crushinator and Bom Boy Factory
Short answer: No, you can't activate Crushinator when you are forced to destroy the factory.

The Crushinator has an ability that you can activate. That activation has a cost (destroying a room). When a hero enters a room, you can choose to activate any spells or abilities you have. After that, you apply damage to the hero and resolve any effects that might trigger, but you can't activate more abilities until the hero enters the next room.

So when the hero enters the factory, you could choose to destroy it at that time, but then the factory would not deal damage to the hero. If you wait for it to deal damage, it will then be destroyed by its own text and you will not get a chance to activate the Crushinator's ability and pay for it by destroying the factory.