You do not sue the insurance company. Any suit is filed against the At Fault party only. The insurance company will defend their client and pay damages according to the terms of the policy.
yes. you can sue an at fault driver if his insurance company refuses to pay your claim. it would not be proper to sue the insurance company.
If you have comprehensive insurance, your policy will cover the damages (less a deductable). In this case, your insurance company will sue the at fault driver. You can also sue the at fault driver for damages (if you do not have comprehensive).
They can pursue him civilly, and the not at fault driver can also sue for damages.
Yes. See an attorney, before they sue you.
then sue for delay of action!
They can, but you can sue the other driver for damages.
The only step you have left is to sue the driver of the other vehicle. Keep in mind, it is your responsibility to prove that the other driver was at fault.
You don't. You sue the individual. The insurance company is obligated to take care of the obligations of the individual.
The insurance companies usually settle each claim independantly. Your insurance will pay yours, the other co will pay theirs. But your insurance will go up. If you have only the required liability insurance your company will not pay for your damage. If you do not have comprehensive and collision, you may have to sue the at-fault driver to force his insurance carrier pay. If you have coverage of your own, you can file a claim with your agent and immediately collect the damages (less your deductible) and your company will sue his if necessary. If and when they win or receive a settlement, you will get your deductible back. Also, if the other driver is determined to be at fault, your rates should not increase.
What happens when an insured driver hits someone depends on the state you live in. In a no-fault state you present your claim to your insurance company for payment. In a tort state, you would sue the driver for compensation. If you have uninsured driver coverage, then your insurance company should cover you and/or your vehicle, up to a certain amount. You should check with your insurance company to be sure.