I would assume that there are multiple exits to the tunnel, as it would be stupid not to case of an infiltration. As for the Third Sister, she likely simply figured out where the tunnel would end and went around the normal way to get there before Leia emerged from the exit.
As for the ending confrontation, I would imagine Vader wants a fight, and all he sees is an old man who is too unconnected from the Force and unwilling to truly fight back, so he simply let him go. I'm assuming by Episode 6 Obi-Wan will realize he needs to confront Vader and gets it together and we get a real lightsaber fight between the two before Obi-Wan escapes again.