In an accident, advice dealing with other ins company

Geico loves to use their preferred shops. The adjuster may insist that you have the car fixed at their shop. Legally, you are not obligated to have the repair done at their shop. You can take it where you want it fixed.
As for prices, I have found that adjusters will go to ebay to get an idea of what the parts are going for.
They're notorious for low-balling and using the cheapest they can find.
GEICO has attempted in the past, to just buy you off. Telling you that you have a "used car".
The good news, you are the claimant. You control how this goes. Keep in mind if the insurance co. doesn't play ball, you go tell your neighbor you have to file a lawsuit against him. He'll panic and stress the adjuster.
I hate to say it, but I've seen it happen in the past, way to many times.