In an auto accident does the insurance company pay damages to whom will do the repairs or to the individual driver?

It depends. In MOST cases, the insurance company will have someone (called an adjuster) assess the damage on your car and write an estimate. After that, your insurance company will contact you on which bodyshop you want the work done at OR sometimes they will pick one for you. The company will then contact the shop who will in turn contact you giving you the ok to bring the car in once they have the approval from the insurance company to begin body work.