If you're casting a Room with escape, you choose which half to cast, then pay the appropriate cost plus exiling three cards. The same is true for split cards, adventurer cards, and prototype cards.

If a card with escape is put into your graveyard during your turn, you'll be able to cast it right away if it's legal to do so, before an opponent can take any actions.

If a card has no mana cost, its escape cost is an unpayable cost, so you can't cast it for that cost.

Once you begin casting a spell with escape, it immediately moves to the stack. Players can't take any other actions until you're done casting the spell.

If a card has multiple abilities giving you permission to cast it, such as two escape abilities or an escape ability and a flashback ability, you choose which one to apply. The others have no effect.

If a spell you're casting with escape has an additional cost of discarding cards or sacrificing permanents, you may exile cards discarded or sacrificed this way to pay that part of its escape cost.

If The Master of Keys is no longer on the battlefield when its second ability resolves, you'll still mill twice X cards.

If you cast a spell with its escape permission, you can't choose to apply any other alternative costs or to cast it without paying its mana cost. If it has any additional costs, you must pay those.

After an escaped spell resolves, it returns to its owner's graveyard if it's not a permanent spell. If it is a permanent spell, it enters and will return to its owner's graveyard if it dies later. It can escape again.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as an escape cost), add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was and no matter whether an alternative cost was paid.

Escape's permission doesn't change when you may cast the spell from your graveyard.