Hi, Alex; Yes, the caliper piston must turn, usually with a bit of down-force at the same time. There is, of course, the possibility that the caliper is 'frozen'. That would also explain the uneven wear. Reman calipers aren't very expensive, and some come 'loaded' with pads. Each time you use your e-brake, the pistons rotate outward to take up any slack in piston travel, but not overtighten.
I own a 2015 Mazda 3 sport 2.0(skyactive). I'm working on changing the brake pads and noticed some abnormal wear. The rear brake pads are unevenly worn off and the rotors is severely grooved. I got new rotors and brake pads but I can't compress the caliper piston. It's one that needs to be screwed in. I use the universal box that I've put on a ratchet and I'm trying to screw it back it, but it just spins and won't compress. I'm hoping ai