disc brake pads actually touch the rotor at all times there is no clearance, well there better not be anyway you'd get a loud chattering noise if there would be any clearance.( believe me i have changed alot of calipers because of loose pads)
however the pads are just barely touching and that is the noise you are hearing and yes the noise gets quieter the longer you do not use brake.
when you use the brake you apply pressure to the piston behind the pad pushing the pad hard against the rotor. when you let off the pressure drops but there is nothing to pull the pad back it just sits there and rubs lightly and eventually backs off enough so theres no noise.
cars. bikes ,trailers all do it, all normal
as far as spinning the wheels go, as long as you don't feel an abnormal drag you are ok. there should be a light drag.