Could be the car just using "shore power" when plugged in and active. It's not charging in that situation, just drawing power from the grid instead of the battery. But it does show the incoming power on the screen, so it looks a lot like it's charging. That stops when the car turns off, soon after you leave in most cases.
The "dancing cars" only dance when they are stationary. I think this is the old problem of detecting stationary things, only with cameras instead of radars. 3D vision through one camera can kind of be faked if things are moving, either you or the target car. But if everyone is stationary there's no simple way to pull distance numbers from a 2D camera. And apparently Tesla is not building a 3D model of the environment and simply remembering where everything was while stationary. At least not for this display. Just one possible explanation.
If the doors/fob are behaving differently than they used to a reset might be in order. That's the first thing to do when strange things happen.