How do I finish Diplomatic Immunity?

After you escape the party, either kill everyone in your way to obtain the key, or sneak to the room with the hostages. In the instance that you took the stealthy way, you will need to wait a little longer with the Thalmor to enter the room and shout out that they know your plan and threaten to kill the wood elf who helped you. Perch up with a bow and kill these people to save him. WHether or not he dies, they have the key to the hatch that the prisoner tells you to go through. If he is saved he gets killed by a frost troll after you drop down through the hatch.