I am the office manager at a body shop and deal with these issues everyday.
There will be NO Carfax history hit. Are you going to tell them? The 1994 Driver Privacy Act prevents insurance companies from sharing claims info with 3rd parties. Only the vehicle owner can release that information to ANYONE, including the body shop he choses to make the repair. Carfax is a joke and will never have accident claims information, only public DMV records. IMPORTANT QUESTION: Who is the insurance company? That will determine, more than anything else, how your vehicle is repaired.
Don't just accept a check and walk away. Every repair has the potential for additional damage upon tear down and the need for more parts. This becomes a "supplemental damage request" and is reviewed/reinspected by the insurance adjuster, documented and okayed. You can't write what you can't see, it's technically insurance fraud. Also, what's listed as a "repair" on the original estimate can easily turn into a "replace" once work has begun and it's determined to be more cost effective to replace instead. That could easily happen with your fender. You also have 12 months from the date the claim was filed to submit any supplement requests for additional accident damage that surfaces after the fact. And, of course, the old "diminished value" allowance that has already been mentioned. Don't be afraid to wheel and deal with that: replace my fender instead of repairing it and I won't ask for diminished valve money. Got the idea? Good luck!