You can leave in whatever way you want. Usually people go by foot or train. But special missions warrant use of Jennifer as a portal. This happens rarely, but you definitely have permission.

As for Venator: Algon makes a point of taking very good care of his guild members (Except for the young-bloods of course, hard to keep track of all those idiots. Ha!)
So he's probably on the bottom of the list of chores you get for punishment. Some poor smuck with a red shirt is going to have the worst day of his life.