Yes anemone sting. same like chili is spicy, and people still eat it. An anemone sting won't kill. I have feel the pain of a fire coral scratching my chest and it hurt but it won't kill you.
a healthy anemone won't get stuck. I you have all she need in your tank, they won't even move. When an anemone get stuck on a power head is becasue they are reaching for light. Power head are ok with anemone, just get a good light for them and keep the water parameter at your best.
Some anemone require more than others. It depends on the specie. They also requiere water movement.
Anemone can be in a tank with coral, BUT!! with a lot of care. If the anemone doesn't receive the light or the water current they need, they will roam all over the t ank looking for the best spot. During that, coral can be damage.