Do you have to get an estimate for repairs from the other persons insurance if they hit your parked vehicle and there was a witness and a police report proving they were at fault?

It depends on what repair option you choose with the company. If you do not go with one of their shops you will have to get an estimate done by either one of their adjusters or your shop of choice, depending on the state. Some kind of estimate has to be done so they know how much to pay for the damage.