Answer:
On your way out" means "as you go out/leave the room, or the building". Most often this would mean that you should lock the door after you have gone out of the building and shut the door behind you. So "lock the door on your way out" really means "Lock the door immediately after you have left the room/building". Which means that it can definitely be considered as giving an order.
D. The person rejected his family but later returned. It is a reference to the biblical story found in Luke chapter 15.
"dependency reversal in noun-attributive constructions" (DNRA) is used to refer to possessive-like attributive constructions (of the type (that) idiot of a doctor), with the attribute surfacing as the formal head and the semantic head surfacing as the formal possessor.
