If I am reading your question correctly you have nothing to worry about. I don't understand why you would be worried about someone coming after you. From your statement your car was legally parked and someone hit it and their insurance should pay.
In the UK it can, if the driveway is private property.
If the vehicle is not being driven you are not required to have insurance. Many people however, do still carry, comprehensive coverage on the ''parked or garaged'' vehicle. This coverage protects you from theft, weather, fire, vandalism etc.
Not if you own the driveway. Your property, your land. IN UK you must tell DVLA that the vehicle is off the road by submitting a SORN
if it there fault there insurance pays
If your "full" coverage includes Collision coverage then the answer is yes, or if you don't but do have Uninsured Motorist Property Damage coverage then the answer is also yes. I think some states have the UMPD listed seperately on the policy even if you have Collision coverage.
The fact that the car was illegally parked doesn't matter. The driver of the moving car was responsible to adjust their driving to the road conditions, and to ensure it was safe to proceed. This accident will be the fault of the uninsured driver.
Auto insurance
No. Homeowners policy specifically exclude automobiles. //
I parked my car in the driveway
tell your insurance company and the police and your insurance company will pay everything except the deductible. If you have full coverage than your insurance is required to make good on the damage. It is up to your insurance company to try and get their money back from the uninsured driver of the other vehicle.
They are.
If you have full coverage on your car, then your insurance should pay. But if all you have is liability insurance, then no, it won't pay to fix your car. But there is a chance that your uninsured motorists coverage will pay for the damages, if you have it.