Are the brake pads supposed to touch the disc all the time, or should they be adjusted somehow?
While rotating my rear while on the centerstand, I noticed that it has a very quiet rubbing sound from the brakes... except for about 1/4 rotation :-/
Yes, but just ever so slightly. The hydraulic pressure applied to the lever (front or rear, doesn't matter) pushes on a piston which has the pad on top of it. But when you stop putting pressure on the lever, there's no "return" leverage. So the pads just graze on the rotor.
I can't speak about much, but I'd think if they aren't rubbing 1/4 of the time, the disc itself might be a little warped. You can probably check, but I wouldn't be too worried.
I've noticed my fronts rub and make noise when I'm rolling the bike, but after 15 minutes of riding without using them, there's no warmth in the discs.