yeah, you definately don't want to touch anything or even pick off the deer hair. The adjuster will need to see some evidence of a deer.
As for getting things fixed that the adjuster doesn't catch, the body shop of your choice will have to submit an ammendment to the ins co. It usually goes through without problems though.
If the ins co doesn't pay for a complete repaint, that doesn't mean that the body shop can't do it. It would just have to come out of your pocket which will be filled with the money they just gave you.
I think it still happens but it this isn't supposed to. You can take your car to any body shop or frame shop of your liking. However, the insurance companies do have what they called preferred body shops. It's usually a place that pays a certain amount to be on their network and they have to have a frame machine and other things. Some places will tell you or make it seem like you have to go to one of these places and that is illegal.
I'm sure you know this stuff already because of your deer count but I'll say it anyway for others that may not know it.