Platys and tetras are known for fin nipping. Tetras are also schooling fish. In the absence of a school, they can become nippers due to stress. You really should get them a few friends. 4-5 of each type of tetra is much better than 1. Platies are just plain aggressive, but they aren't schoolers. Don't get any more platies.

I could not see your video, but mixed fruit tetras are injected with dye. This process results in pain, occasional internal problems, and sometime death. The fish lose their color in a few months. Often it reduces their lifespan by half. I'll assume that it is a white skirt tetra with dye, as I can't see, so it may or may not school with other skirt tetras.