This is best answered by referring to the language of your private sales contract.
What will happen when your property is auctioned off?
YES.
Yes.
Yes, repossessions can (and often do) occur on private property. There are limitations imposed on the recovery agents, and they know how to plan accordingly. IMO, better that car (which is actually the lien holder's, which is why it can be repossessed in the first place) be repossessed while you're at home than while you're out in public somewhere and left stranded.
Yes. If the person repossessing the car finds it then they can take it!
Yes. Your car can be repossed from anywhere but locked garage. The repossesion team cannot break in to a garage or other locked building. But they can still retrieve it, by serving you with papers to release the car. Keep in mind, the bank or finance company that gave you the loan for your car actually owns your car; you do not really own it. If you do not pay your loan payments and are threatened with repossesion, they have every right to get that car from you, even as it is sitting in front of your apartment, which is ostensibly private property. A friend of mine once had his car repossesed from outside his workplace while he was at work; he had to bum a ride home.
Court?
A car that is actually YOURS cannot be repossessed, as it's paid off. If you have a vehicle being repossessed, they're able to do this because it's actually the finance company which owns that vehicle and possesses their title. A recovery agent can, on behalf of the lienholder, go onto private property in order to recover the lienholder's property - with limitations. They cannot cross a locked gate, and they cannot enter a locked building.
The private sectors tax revenue
Dealers pay low(wholesale) prices at a public auction, private might be better. A lot depends on the car and the markey for it in your area.
A slow speed limit cannot be enforced on a private road in the state of Virginia. You can put a sign up but is will not be enforced by the state.
Northern Virginia Community College is one of 23 colleges within the Virginia Community College System (VCCS), which is governed by the State Board for Community Colleges. Therefore it is a public college.