Your collision and comprehensive cover your vehicle.
If you have collision coverage then yes, car insurance companies will cover the damages caused to your car, or medical treatment required, within the stipulations of your policy. However, if you don't have collision or underinsured/uninsured motorist coverage, then you will not be covered for the damages to your property or self.
Comprehensive Coverage.
If you have an applicable coverage it should cover you whether you run away or not.
As long as you have collision coverage, they will. However, if you only have liability, you're on your own. Good luck.
Uninsured motorists coverage is the coverage that is designed to cover this type of accident. Collision will also cover it if you don't have uninsured motorists coverage on your policy but you may be charged with an accident on your policy. A-Plus answer Comprehensive Coverage.
Sometimes a deductible will cover a hit and run accident if the driver does not have the license plate number. More often than not, they will not cover the accident because there is no proof of the accident.
No. Unless you killed somebody's pet deer, liability insurance is no value. Liability insurance covers the damage you do to somebody else's property or person. Collision insurance covers damage to your vehicle when you strike an object or animal or when your vehicle is damaged by someone unknown, as in a hit-and-run accident.
That would be considered a hit and run which would fall in the comp/coll portion of an insurance policy
In the US That would be considered a hit & run and if there is no id on the other party then your own collision coverage will have to apply for the damage; that is if you have collision coverage on your policy. As with all things insurance, it is always best to speak with your insurance company directly. Other countries have different rules, check with your insurance company.
The person that the vehicle belongs to.
It should, according to carinsurance.com: http://www.carinsurance.com/kb/content36844.aspx"Collision coverages typically cover damages to your car when your car hits, or is hit by, another vehicle, or other object. A hit and run that clearly shows another car or object collided with your vehicle should be covered under your collision coverages."