You do.
nothing
Yes, private property does not obsolve you of your responsiblity.
In the UK it can, if the driveway is private property.
yes
you are
private property impound - possibly due to parked in a private lot
The person who caused the damage.
The driver that hit the parked vehicle would be at fault.
Whomever backed into it is at fault.
If a car is parked next to my fence is that OK?
The person who hit a parked vehicle is at fault.
A parked car almost never crashes into others or does anything else that prevents other drivers on private property from stopping in time to avoid hitting it. Therefore, the fact that it may be "illegally parked" usually has nothing to do with why someone negligently crashed into it.