Nokia used to have this, and they recently added it to their newer Lumia models, called "Glance". It's cool, can show time, wallpaper and notifications.
Yes. But at least for amoled, it can backlight only the shown pixels.
My Lumia 920 has IPS LCD, so it need to backlight the entire screen. But still, the energy consumption isn't that high. It turns off the screen when in the pocket. I have more than enough juice left at the end of the day.
