Putting the car into park while rolling won't cause this type of damage, if anything it will snap off the parking pawl _after_ the car comes to a stop. When park is selected while rolling, the pawl will bounce off the parking gear until speeds are low enough that it finds a slot.

This is long term wear and it almost looks like there is a spacer missing ( governor gear ? ) in the stack up. I have seen situations where a nut or bolt was tight but it didn't compress the joint allowing things to move around.

As for the shifter not moving, the parking linkage / pawl assembly is likely not proper causing the park rod to jam.