are the pads rubbing up against the brake discs?
the pads are always touching the disc. that's one of the reason discs typically feel more responsive than drums.
I suspect you still have some air in the line(s).
this would not cause his problem.
Did you remove the cover of the brake fluid reservoir when you pushed the pistons back in the calipers?
this does not cause any problem. the master cylinder will vent on it's own, the cap is designed for it.
i would take the brakes back apart and make sure that both the pad slides and caliper slides are moving properly. you didn't have to use force to get the caliper back on, did you? perhaps the aftermarket pads are a bit thicker than stock.
if you can't find anything that would be causing the pads to stick, maybe you've got a bad caliper. i've seen people damage calipers while pushing the piston back in, though i'm not sure how the hell they did it. your old pads weren't completely gone, were they? (i.e. caliper piston was pretty much extended to the max)