Yes, if your car is totaled, and the title reflects a "first secured party of interest," that means the car is collateral on a car loan. And the insurance company is required to protect their interests.
Sometimes they will send one settlement check with two payees listed, and sometimes they will issue two checks, one to you and the other to the loan company. To do that, they would need to contact the loan company to get the pay-off balance on the loan.
You need to find out what the pay-off balance is today on your car loan, and compare that to the amount of the settlement proceeds. You will get any money that is in excess of the pay-off balance on the car loan. If the pay-off balance is MORE than the settlement, then you get nothing. In that case, we would say you are "underwater" on your car loan.
If you are "underwater," then check and see if you have any GAP insurance to help you.
Yes. You can have them sign a waiver saying as much. Also, fun fact, parents are not liable for the torts (personal injury or property damage) of their children. Generally these are drafted by lawyers, but for something small like this, you can simply write a note that says the above and have the client sign it. Unfortunately, as a minor, you cannot legally waive harm that may come to you because minors cannot bind themselves to a contract.