Am I at fault for hitting another driver’s door as I pulled into a parking spot?

How can both the hood in front and the tail light in the rear both be damaged, especially by a door that probably impacted the side of your car? In any case, the driver of the other car should not have open his door without first checking to be sure it was safe to do so. But you would be required to properly enter the parking space. It seems to be that you may have been too far from the center of your space [unless it was abnormally narrow]. If you have liability coverage, your insurer will pay for all the costs of repair but if you were at fault, they will not cover the deductible. They might also increase your premium rate.