The driver did not shoot him. He does look back but what some think is a gun is a reflection off the head of the guy next to him. The driver's left hand is on the wheel the entire time. You can see this. You can also see his white shirt. Shooting with his right hand would be awkward from that position (and the video claims left hand anyway. Because we can see the driver's white shirt we know he did not shoot with his left hand because his left arm would be crossing over his body, closing his suit coat and making the shirt not visible.

Jackie reportedly was on the trunk of the car because she was picking up pieces of her husband's head/brains.