Okay so during the questing phase, I turned over east bight patrol. His threat of three is instantly added to the decks total, correct, for quest resolution?
East bight patrol then stays in staging area until engaged one way or another, yes?
After quest resolution, say that I exhausted all of my heroes on committing to quest progress. Can I still travel after that, in the next phase (travel)?
Yes. Travel just means you get to move one location from the staging area to the travel area. This has +/-, it removes that location's threat from the staging area but now you have to quest its quest points before you can add anymore quest tokens to the active quest.