The driver who hit the pedestrian is liable, not their insurance company. The drivers insurance company will normally be responsible for payment of valid claims up to the policy limits for which the their insured driver is found liable.
If someone causes damages to your property, they are liable. This means, however that you have to deal with their insurance company directly, rather then your insurance company doing it for you.
no
Yes.
It depends on who is at fault. If the police car had his lights on, or otherwise was in the right, then the registered owner of the car at fault, will probably be liable, no matter who is driving, and, your insurance may not have to cover it. If the driver has proper insurance, they may cover it, though. And, if they had keys to your car, then they had permission. In my experiences anyway, that is the way the law views it. Answer If a car is taken without your permission it is stolen, no matter who is driving it or whether it is reported stolen. You should not be liable for any damage to the police car. How your insurance company deal with your claim is between you and them, there is no general rule. In the UK there is a process for recovering uninsured loss.
You both are.
yours
You or your insurance company. The owner of the stolen vehicle would not be responsible because their vehicle was stolen and the driver of the stolen vehicle's insurance would not cover it because he was driving a vehicle that was not on his policy and he did not have permission to drive.
Absolutely yes. You are ultimately liable for any damage you might have caused whether you had insurance or not. The only difference is that if you had insurance your insurance company will pay up to the policy limit for damages you might be liable for. So you can get sued for damages whether you had insurance or not.
It was your car so your insurance will have to pay. Never loan a car out to someone who is not on your insurance policy.
Turn it into your insurance company first. Your insurance should handle everything. The way it usually works is his car is supposed to be insured so contact the "borrowed" cars owner and see if the driver is covered, if not the borrowed cars owners insurance may not pay and the owner will be liable for the cost of repairs, etc.
Generally speaking, no the owner's insurance will not be liable, BUT in some jursidictions, the owner may be liable, IF they didn't take basic care to prevent the theft of their car. So if the car was left unlocked, or the keys were inside the un-locked car, the owner MAY be liable for damages casued by the stolen car. The theory in law here is that the actions of the owner created a situation that allowed the thief easy access to the instrument that caused the damage, namely the car. In some cases, the court may find that the percentage of the blame will be shared by the owner and the thief, fifty fifty, or some other percentage, determined by the Bench. Shared guilt is the concept here.