Some insurance companies will sell the car back to the owner. Others sell the totaled car to a salvage yard.
Typically you need a car with insurance to get a title loan. If your car is totaled, the loan company are entitled to that money since they hold the title for your car.
If you have the proper insurance or you were hit by someone you will surrender the car and the title to the insurance company and they will pay you the actual cash value of the car before it was hit.
If a car is totaled in an accident and only liability insurance is present, there is a chance that the other party's insurance will pay for the vehicle if the accident was their fault. If a car is totaled, but no others were involved, then the responsibility falls on the registered owner. This will not release the registered owner from paying for the vehicle, either, if money is still owed on the car.
If you want to keep a totaled car, the insurance company will determine the salvage value and deduct that from your settlement check. You can still get liability insurance (if there are no safety issues related to the damage), but not collision or comprehensive unless you have the repairs made.
Read your policy.
It would depend on why the car was totaled and who's fault the accident was and what time of insurance do you have PLPD or Full Coverage
The insurance company. They have in theory bought the car or what was left of it.
No, they will not.
You will get actual cash value for the car and will sign the title and car over to the insurance company, unless you wish to buy it back for a reduced payout.
Full coverage auto insurance covers everything. If the car is totaled they will will replace it. Liability auto insurance will only cover medical bills, and not the car if it is totaled.
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.