Hormones Lovebirds

Lovebirds do not do well as single birds. It may be one of her problems.

This isn't true, depending on the care provided. Kept singly they do require a lot more attention to remain happy but they do fine. A glance at these threads reveals several examples of single, happy, well adjusted, companion lovebirds. Lovebirds do require company to be happy however (human or bird,) so it is true a bird left alone will not do well.

As for her hormone problems, I also find it strange they are happening so young and without things like a nest being available. Still, it might be a matter of waiting it out for a while. It's my understanding that the first hormonal cycle is the hardest on both the bird and it's people. She's young, and like a teenager could have trouble with that sort of thing. Still, I only have experience with one bird, also a single female lovebird, and her first outburst would have been over 10 years ago so my memory could be spotty. I do remember my hands being covered in little bite marks, if that's any indication of trouble. XD One thing I do remember doing is when she would get humpy, I would put her back in her cage for a few minutes. Not for long or as punishment, just give her some time to get herself under control and snap out of it. She would go into some kind of humping trance and I would have to sit on my hands (the object of her affection...) just to get a reprieve! Maya has some good advice, try rearranging her cage or moving it. It sounds like, with all the biting, she is very territorial. Does she have a toy or area she is protecting or trying to mate with? If so, it should be removed or blocked. Like you've already done with your ponytails, just removing these little things can maybe stop her. Is she trying to gather nesting material too? If so, keeping her away from things she uses could also help. Another thing you could try is a sort of simulated winter, put her to bed earlier to make it seem like there is more darkness.

Finally, if all else fails, she should eventually stop being hormonal... until next year. In my experience, it's gotten easier with time too. Not only has Peanut (seemingly) learned to control her urges better, I've gotten better at avoiding her triggers. The past several summers have gone humping and egg free.
Still, it would give you another year to work on your bond with her, and foster more trust. Hopefully as she trusts you more and matures even when she does get hormonal she won't be so quick to attack.