A school administrator cannot search your car, or your bag, unless he has your permission (Although not letting him is basically admitting guilt). Off the school premises, if he searches your car, he is basically breaking and entering your vehicle. He would need to call the police for a warrant.
Yes, police can tow a vehicle parked on private property if it is illegally parked or if it is obstructing traffic or posing a safety hazard.
Have it towed?
Depends how long it has been there.
You do.
Yes, private property does not obsolve you of your responsiblity.
In the UK it can, if the driveway is private property.
The driver that hit the parked vehicle would be at fault.
Yes, the police can tow your car from private property if it is parked illegally or if it is blocking access to the property.
yes
you are
Yes you can, as long as its not stolen.
The person who hit a parked vehicle is at fault.