From the Catacombs

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.

In a Two-Headed Giant game, if both players on a team deal combat damage to the player that has the initiative at the same time, the player with the initiative will choose the order of the triggered abilities. Then, as those abilities resolve, one team member takes the initiative (and ventures into Undercity) and then the other team member does the same. The last player to take the initiative keeps it until the initiative changes again.

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.