The appendages on the back end (kind of like a tail, but they are actually gills) makes it a bit easier to tell the difference between damselfly & dragonfly nymphs. Damselfly nymphs have only 3 appendages (soft) on the back end. They usually have long, slender bodies. Dragonfly nymphs have 5 stiff appendages on the back end, and usually have bulkier bodies.
I wouldn't say they are absolutely harmless. They are predators, and they are experts at hiding in plants. Unfortunately, they can stay in the nymph form for quite some time before transforming into an adult fly. I had a couple bad experiences with damselfly nymphs that managed to somehow get inside a couple of my shrimp tanks (heavily planted). They really did a number on my shrimp colonies (populations dwindled down quickly). As far as removal: physically removing them worked best for me, but it can be a slow and painful task if your tank is heavily planted.