If it "easily came out of the rock," then it was at best useless and at worst a safety hazard, because of the possibility that someone might naively trust it. Removing it was a public service.
Is it even wise to use pitons that you find in the rock?
I use old fixed pins as pro all the time. If it's on a popular climbing route and has obviously been there for decades, the reason is probably that it's stuck solid and will never come out. You'll even see them described in guidebooks and drawn in on topos. However, I wouldn't use one as a non-redundant rappel or belay anchor.
Should you clean your oun pitons while cleaning the rest of you gear?
Yes. The more relevant question is what the local climbing ethics say about whether you should even place pitons. Most people in the last 40 years have practiced clean climbing. Pitons leave behind pin scars, which mar the rock.