I use the iPad as a panel for Home Assistant, as a result, pixel burnouts are already visible. At night the elements can shift a little and change color in special mode - this would not happen
Don’t know, how to with ipad, but with my two android tablets i use the built in screensaver. The tablet displays a clock, moving around the screen. Only, if someone stands in front of it (using the built in camera as motion detection), the HA dashboard is displayed.
Should be easy to do with ipad too 
No, because iOS has more camera restrictions, and can’t open camera every time
For the screensaver to be usable to protect your screen it doesn’t matter if the camera can be used (or not); it’s just convenient that the screen wakes up when there is motion.
There was a HA screensaver that could be what you want but it’s some time ago that I’ve bumped on it so you might find it searching on the forum.
Yes, it will be nice if screensaver will be inside mobile app