Yep, it stays in one spot–usually on it's side trying to brush the wall of my beach ledge and steps. If I'm not watching it, it could be there for an hour. Haven't seen any damage related to that spot cleaning either on the PebbleTec or the robot.
Mine gets stuck right dead center, treads and brush just spinning. It would run until battery died if you're not there. Not a big deal, but my guess is I'll be watching with a beer in hand or in the pool (with beer in hand).
Thankfully, no.
My wife's family is from Oklahoma and we decided to move out here when I retired from the AF. As an FE, I was on the C-5 which used a long, LONG cord.