The GW Parkway is a National Park; no grey zone about it (except for the fact that there are no signs warning you that you areabout to becomea criminal). The portion of the parkway which is Washington St. in Old Towne belongs to the city of Alexandria and is not a NP, from what I gathered in Alexcabbie's thread.
Don't know about the rest. I also wondered about US Rt. 211 in Shanendoah.