1. Yes it should work. I would opt to run component video DIRECTLY from STB to TV in LR, and use spdif for sound. Then run HDMI directly* to bedroom TV. Forget the receiver entirely for video, but use for main area's speakers (spdif). I don't ever remember setting any source up that didn't send it's signal through all of its outputs simultaneously, though I'm sure there must be cases of it.
2. Scrooed.
EDIT: regarding 2, or even 1 for that matter, why does everything have to go thru a receiver? Why not just hook up the X box where it needs to go directly or something? Whether that necessitates a component video or HDMI video switcher (they can be controlled by remote too . . .)