When my DS recognised letters, numbers etc I thought all kids did at that age, I had nothing to compare to really. It took me a while to figure out he was a bit ahead of the curve. I don't know about "gifted" though, his nursery teacher put him on the gifted and talented list for the attached school (they don't do G&T in nursery but she expected him to move to their school where they do have a G&T programme) not long after he started nursery when he was 3, and he was already reading fluently then, but he didn't go to that school and where he is at they don't have a G&T programme and don't talk to me about his development. So, I don't know. He is ahead for now but I just tend to think by the time they are 18 no one will care who started reading at what age or at what age they could tell the time etc, yk? Everyone will be able to do it.
Certainly though, what you have said about your DD craving for books, it is just like my DS. 30+ books in a day I can easily believe.
My mum made little flip books from flash cards (a hole in the corner so they all held together on a loop), I wondered what on earth she was bringing this stuff to the house for, letters, numbers, colours, shapes, animal pictures etc...but left to his own devices he would go to his toy/book box and dig them out, bring them to an adult and demand to be told what each one was and when we'd finished he'd just flip it all back to the start and demand again. he had his own choice of toys to play with etc and of course did play with other things but he was SO keen for information he would just complain and complain if we wouldn't do it - just easier to give in and say the words yk?
It sounds like Bt for you was calmer without the books, but still took her a long time to wind down to sleep. She might perhaps have a very active brain whirling away sorting everything out and storing all her memories of the day. I don't have any suggestions for that I'm afraid. Mine generally fell to sleep very quickly (apart from the usual phases) but he often woke in the early part of the night having some sort of developmental dream, once he was verbal I could get a sense of his dreaming by what he shouted out in his sleep (letters, numbers!!), he must have been processing it all in his sleep. Perhaps your DD is processing prior to sleep and it's just her way to take a long time to relax?
Sorry I don't seem to be much help.
I do know though that many LOs moving to one nap do get OT over time and eventually the nap or night lengthen to accommodate the amount of sleep needed, same with the nap drop, they don't seem to get as much as they need to begin with but eventually lengthen the night.
The teething too though - it just goes on and on doesn't it, and as soon as they come into a lighter sleep they wake with the discomfort of teeth moving even if they are not cutting at the time.
Is there any light getting into her room in the morning? Could she sleep later in a darker room?