Backstory:
Since purchasing the bike, there's been an odd high-pitched tinkling sound from the rear brake caliper, like something was loose in there. I could even hear it at relatively high speeds. However, the brake worked just fine, and I read on here somewhere that the calipers don't have a retainer spring and the pads kind of rattle anyway. Or something to that effect.
So I pulled the brakes apart, and the pads fell out, and I found this:
It had been sitting in the caliper, between the pads, I believe, like this:
Note the grooves worn through the metal by the brake rotor in the spring in the first picture. I assume that this was the source of the noise. I've never done the brakes, so I'm sort of inferring here, but I think the last time the brakes were serviced, this spring was put in upside down. It seems to fit in there much better and keep the brake pads in place when it's placed in there like this:
Have I got this right, or am I way off?
Also, I'm not sure if my pistons are stuck. Should I be able to hold the caliper in my hand and pull the pistons out with my fingers or pliers? They're completely torn down since the lines both got air in them and drained (and the bike is torn down), so reassembling them and refilling them with fluid and checking them that way isn't an option just yet.
Thanks in advance.