What's up with my zebra finches? Fighting? Please help. :(?

DEFINITELY separate the two. I had two zebra finches that did the same exact thing. She would chase the other one around and it got to the point where the bottom of the cage wasn't even safe for the other. She would just continue chasing her, even feather plucking her. I separated them a couple of times and let the one's feathers grow back in, but each time I put them back together, the one continued to chase the other. My biggest regret is not permanently separating them because the one ended up dying. I don't know if it was the stress, or what... but I'll never be able to forgive myself. Therefore, not only for your bird's sake but for your's, keep them in separate cages but next to each other.