Yup, they will nip anywhere they can. The fins are the most common areas as usually one is swimming away and the other behind can only grab onto the fins. It's sneak attacks that gets them nipped other places. Silly fish.
And yes, the alpha will remind the others often who is in charge. If you decide to replace the girl with another, make sure to rearrange the tank prior to adding her in. I would cup them all, keep them out for a bit, then float all their cups together in the tank, releasing the more gentle ones first.