The clock battery is not drained when the Wii is on. When the Wii is off its entirely powered by the coin cell (in the Wii this is a CR2032 3V cell). I haven't done any current measurements, but I'd imagine that like most RTC circuits, current draw is very negligible when powered by the Wii. Bluetooth similarly would be almost unnoticeable, but I'd like to see some measurements if someone has done them.
LCD backlight brightness can be adjusted usually via a daughterboard that comes with LCD panels. Aurelio's DD project will allow for screen brightness adjustment straight from the Wii side of things, though. Something to definitely look forward to!