I'm sure it's possible, just how much work is the real question. Trying using an app like es-file explorer and long clicking on a photo and set it as wallpaper. Not in front of my mi box to check.

By default, the background image is in the leanback launcher apk. This differs on the Shield though as the background image is found in the Nvidia Customization.apk

No proper solution that I know of. I think that a workaround using the recommendation system could work, some developer may make an app that makes a persistent notification that when highlighted would change the background. It's far from a perfect solution but it might work.

Nope