I have too agree. The peeing and pooing could be medical, but if the litter box is being moved that is more then likly the cause.
As to the running try our house one or more of the kids are running or bouncing off the walls, ect. at any given time. Chessie's favorite is to walk into the TV room and attack the corner of the bath room about 5 feet up.
The other day I found Roz almost to the ceiling on a corner between the kitchen and sitting room. She was just having a great time. I had to laugh as Lucky was just sitting there watching. Knowing that she was going to be in trouble. She just looked at me as if too say YA, SO.