Sorry about your luck with the car, but main thing is nobody really got hurt or worse killed. By the looks of it, it sure was one hell of an impact.
I am in the insurance industry and if you are not at fault in the accident, you automatically get a rental. Again, by the looks of it the car will be a write off. When a car is written off, the insurance company technically only has to pay for the rental car till they make you an offer on the pay out. They usually give you a few extra days. What company are you insured with? That sometimes makes a difference.
Provide the adjuster with some prices from autotrader or ebay and they may base payout on those stats, but usually they pay out based on year, make, model, mileage, general condition etc.