It is normal for the car to move a little before the parking mechanism engauges.
Broken "Parking Pawl"?
that's normal, just the metal cooling down when parked and off.
If you are parked and you want to here the radio without the Automatic headlights on. Some times if you engage the parking brake it will turn off the automatic head lights.
Manual or Automatic?? In either case, most likely the linkage. Manual, might be the syncronizer gear or low on lubricant.
water coming from the exhaust is normal not lots but some
As long as the parked vehicle is parked properly and not illegally parked in any manner, then the vehicle that rear-ended the parked car is at fault. Now if the parked car is sitting illegally (such as double parked or parked in a no parking zone, etc.) then the parked car is at fault or even both the parked car AND the car that hits it are BOTH at fault.
If you are parked on a steep hill or the front wheels are parked hard up against a curb it may cause that to happen. It may take some force to get it out of park. If that fails to work, check for a blown fuse.
The person's who parked it there, (its parked illegally.)Not your fault.
Parked was created in 2011.
If the vehicle is parked on a hill and the weight of the vehicle is being held by the parking gear you may find that it will be difficult to shift out of park. I suggest using the parking BRAKE to hold the weight of the vehicle while parked. Set the parking brake BEFORE you put it into park, or at least before you remove your foot from the brake pedal. That way you are having the parking brake hold the weight and the transmission becomes the backup for holding the vehicle. It should be a lot easier to get it out of park then.
sounds like one of the valves in the valve body is sticking when it gets hot (metal expands). Sounds like a Ford automatic overdrive to me.
It would be the car who had parked illegally because he was not parked in a legal spot.