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 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 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.

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.

If Underworld Rage-Hound can't attack for any reason (such as being tapped or having come under that player's control that turn), then it doesn't attack. If there's a cost associated with having it attack, the player isn't forced to pay that cost, so it doesn't have to attack in that case either.

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 the battlefield and will return to its owner's graveyard if it dies later. Perhaps it will escape again—good underworld security is so hard to come by these days.

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.

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