Doubt you can ask one which hasn't come up before.
1 -In the Commonwealth of Virginia, open carry of a handgun is legal because there is no statute forbidding it, no restriction on OCing in a vehicle either.
2 - No proof of ownership, no registration. You can carry a borrowed gun.
3 - OC in whatever style holster works best for you OWB, IWB, et al - the test is whether the gun can be easily identifiable as such and not be of a deceptive nature i.e. belt buckle gun which would require a permit.
Local ordinances cannot restrict how one carries. - we enjoy a rather meaningful state preemption. Just the carry of a gun is neither PC for a stop, nor RAS of a crime. You can OC in an establishment that sells adult beverages ...and drink, though many of us here discourage imbibing.