if you submit a claim through what they consider proper procedure, assuming you have coverage according to your policy, and they deny your claim, then yes. you can sue for actual damages. depends on tort vs limited tort in your policy if you can sue for pain and suffering. they should pay for it as long as your policy covers hit and run and you don't have a cap.
On your insurance, driver hit TP means third party. This basically means that if you hit anyone, that person can claim against your liability.
Medical or Health Insurance
Which insurance company? If you don't know who it was, who should pay? If it was a hit and run accident, perhaps the police could help. If not, there should be a police report and you can get the information from there.
If the insurance policy is active and valid and the driver is a covered driver then you file your claim just as in any other accident.
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.
Your insurance will have to pay regardless if the other person has insurance or not. You were at fault.
You give it to the police and they will deal with it. Or your insurance company will deal with it.
If what person is driving the person that was hit or the person that hit?
Yes.
Yes. As long as you were insured when the accident happened they will pay the claim.
It is my understanding that the car owner's insurance pays for the person who was hit. The driver's insurance is responsible for the car he/she was driving.
This will depend on the type of insurance coverage. The insurance company can decide to go to court and argue that since the driver was uninsured, then they should not be liable for damages.