Have a small camper trailer. In general, is it OK to park (with car attached) in the various parking lots and curbside trail head parallel parking for AT ?

Ok to sleep overnight in the camper ?

I know a lot of the parking areas are different domains (state parks, national, conservancy, etc). Also understand safety and vandalism.

Old retired guy - I want to do a mix of day hikes and overnights in shelters in area from Roanoke VA south and trying to figure if having this camper with me is worth taking / permissible.

Thanks for any input.