No. Liability insurance will only cover your liability for property damage/injuries to others. In this case, it would cover the damage to the pole you hit. Your liability coverage will never cover damage to anything you own. You would need collision/comprehensive coverage to cover damage to your car.
If your liability insurance is not enough to cover the damages, you will probably be sued by person you hit or his representative for the rest of the damage.
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.
If all you have is liability, you will have to pay for your repairs yourself. If the hit & run driver is caught, you will probably have to sue to get reimbursed.
You do not pay a deductible for the car that you hit. Your liability coverage does not have a deductible.
Liability coverage offers coverage for bodily injury and property damage to the other vehicle and passengers who you hit if the accident is your faulty. It does not cover you or anyone in your vehicle.
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.
If you have an applicable coverage it should cover you whether you run away or not.
Yes, if they accept liability and they will pay up to the limit of property damage coverage.
If you hit a deer, coverage is found in your auto policy in the "Other than collision" or comprehensive coverage section for damage to your covered auto. Liability is available only for third parties that you injure due to negligence.
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.
If you caused the accident, you owe for the legal liability, the other matters are civil & not involving the liability portion of the insurance. They still have a duty to pay.