Nems will move until they find a location that suits their water flow and light requirements. They can be tough to move though, because when they attach, their foot basically forms a hydraulic vacuum on the substrate--if you just try to pull it lose it will tear the nem and cause a lot of damage. I've heard of people using the edge of a credit card to gentle pry the foot lose. From what I've seen, when the edge starts coming off then it will let go. Also heard of people using a power head to blow right on the foot--kind of irritates it and makes it let go.
As far as stinging, yes they do sting and just about anything. They are all Cnidarians which is the phylum of animals that have stinging cells for defense and prey capture. As far as it stinging you the answer is--it could. It depends on species and how sensitive you are to the stings. Even if you are sensitive, generally it feels no worse than a small rash, however if you are allergic to bee/wasp stings, I would take cautions against being stung such as latex gloves or such.
HTH