It sounds like she has negative experiences with cage confinement and people. Most likely she was poked and prodded a lot by her old owner and maybe their visiting friends. That would explain the reflex to nip and people and not liking cages.
If she’s unwilling to chew cardboard, can you line the inside of the cage with cardboard so she doesn’t hurt her teeth on the cage bars? You can cut out cardboard windows and such so it doesn’t block general view as well.
Some rabbits, like my Wick, simply don’t like chewing on cardboard or wood. It’s much better that she eats lots of hay.
I think regardless of diet, any rabbit would jump to get a raisin, haha.
In terms of people nipping, I think she needs to learn to trust people first. There’s an approach that works for some rabbits which is just taking the nip and not reacting negatively to it. A nip is a rabbit’s communication method, whether it be go away or listen to me. If she can learn there’s routine in your behavior (you’re not going to intrusively pet her and prod her randomly), she may no longer feel the need to nip. Rabbits like routine.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.