If you have an applicable coverage it should cover you whether you run away or not.
If you know who hit your car, and they have insurance, then, yes, they should pay for it, so long as you were not parked illegally. Let YOUR insurance company handle this for you. That's what you pay them for.
You do not have to reimburse your insurance company if the accident is the fault of the other driver and the claim is made on their insurance. If the accident is the fault of the other driver and their insurance does not cover everything and you make a claim on your insurance for reimbursement, your insurance will subrogate (collect back) from the other company.
In a case that is like this, the insurance company can pay under uninsured motorist and attempt to collect when the hit and run driver is found. Although it is not your fault the insurance company will keep a record and note if you have a repeat of this happening.
Property damage liability car insurance will cover the individuals car and property that you hit. It will not cover anything to do with your vehicle if the accident is your fault.
It would be your fault, so your insurance company will pay. Unless of course, you have no insurance or you flee then his/her "no-fault" insurance would pay for the damage.
If you have medical, yes because your medical under your car insurance covers your passengers, regardless of fault.
No. PL & PD cover injury and damage you do to other persons and their property. Collision and Comprehensive cover your vehicle.
Typically the person who hit you pays. If they don't have insurance, your no fault insurance will pay for it.
In the U.S., in states that do not have No-Fault insurance: You need Uninsured Motorist coverage to cover damage to your car in case of hit and run. In order to not be held at fault inappropriately, get the contact information of any witnesses, and explain what happened to the police. If there is doubt about who is at fault, the insurance company may decide based on the police report (including what citations were issued). A court decision, including assumed guilt if a citation is not contested, will often determine fault.
The person who hit the car, if "at fault" would be responsible. If the person driving your car was the one at fault, then it would be your insurance that would have to cover it.
Just because they left, doesn't automatically make them at fault. The insurance company claims department will make the determination base on the facts of the accident itself, not about what happened afterward.
If you are not at fault, then you should contact the other driver's insurance company. You may need to involve a lawyer. You should also have insurance. You're an idiot not to.