Well Linux allows more than two users, but that's another issue. You wouldn't be using another user to do this, but simply putting the desktop into a mode where all functions apart from phone calls are disabled.

I think the most workable solution is in fact to have a mode for the phone app itself wherein the touch controls to close the app or return to the desktop aren't visible, and can only be shown again with a code.
I'm not sure that it would be so easy to create something that allowed you to do example #3, though of course you could always just show the background image via the image viewer.