If you have full coverage and total your car will the insurance pay for another car even though the one you crashed wasn't paid off yet?

no

No, the insurance company has a responsibility to the lienholder first, then you get the balance of the settlement based on the local market value of your car. Insurance companies are not responsible for purchasing you a new car and the settlement is based on the value of the car you had an accident in. The settlement is not based on what it will cost to buy another vehicle.