Deb could have a key, couldn't she, as the officer in charge of the investigation? It's still a bad choice of place.
The therapist told Deb that Dexter was her "safe place" that she turned to; how safe will she feel now? That on top of her facing up to the fact that she's in love with her adopted brother...poor girl, what a lot that is to handle.
When this series first started, Dexter killed only those villainous men that the law didn't punish, either because of a legal technicality or through ignorance of their misdeeds. He was doling out a particularly grim sort of vigilante justice. But now Dexter is killing because he wants to. The police know Travis's name; as long as he stayed in Miami, they'd find him eventually. But Dexter has been in a race with the police, needing to find Travis first when he could have just sat back and let the investigation run its course. Is this deliberate, or is it just careless inconsistency on the part of the writers and producers? I can't tell.