It would be incredibly easy for the car to pick a safe, viable spot. All you need are color sensors and if you have two white lines with no yellow or white or orange inside of it, then it will work. And just like facial recognition you can easily have handicap sign recognition on the side of the car. From there any motion sensors will tell if there is a child standing in the spot, and the reaction time of the car can be made to be much better than that of a human. Obviously it wouldnt run out of gas. For a car that smart that is easy to make sure there is enough gas in the car to drive around a parking lot. As for who's liable, obviously the person who owns the car. All this stuff is going to cost a lot, but it can definitely be made to work without any external hardware for a reasonable cost.