Arvel the Swift got away when I released him and now I can't find him to get the golden claw. Any idea where he might be if he escaped with his life? I haven't come across his body and I went all the way to the round door with the lock.

If you didn't help him by getting ahead of him, then he either got killed by the spike wall trap, or by the swinging blades. Check those areas. Also, if he survived THOSE, then the Restless Draugr at the end of the first zone certainly finished him. In any case, he didn't make it into the second zone.

He dies. He can't get away... He was either Dead by the Spike Wall Trap, By the First Set of Drugar, Or the Swinging Axes. You should have caught up to him, by the Hall Of Stories, Unless you just wanted to see what happened. You should have watched the trailer.

If the quest is marked as active then there should be a pointer indicating his location.