1. This is likely from boredom, or too small of a cage like you stated. The larger cage you bought should hopefully help this problem. Additionally, could you add an x-pen onto the front of the cage? If she doesn’t get out everyday it would be nice for her to have space to binky and run around. Adding more toys might help too. You can try hard plastic baby toys, clean plastic lids, toilet roll tubes, brown paper boxes, and brown lunch bags.
2. Is Lux litter trained? If you notice a significant difference in the bathroom habits or consistency of your bunny, the best course of action would be to either call or visit your vet just to make sure there isn’t anything else going on. Otherwise, try moving the water bowl to a different area of the cage, one where she doesn’t typically pee, or invest in a crock type water bowl that hooks on the side of the cage so she can’t pee in it. Water bottles typically aren’t recommended for bunnies as they often have trouble getting a suitable amount of water from them.
3. Grunting is normal and usually happens when a bunny is scared, mad, surprised, dominant, etc. Make your presence known to your bunny by approaching her from the front and talking to her when approaching her to avoid startling her. Avoid reaching in the top of her cage as well, approaching her from the top may frighten her as well. As rabbits are prey animals, hands or other objects approaching from the sky can scare them.
4. Bunnies typically have pretty silent breathing, so whistling through the nose could be an indication she has blocked nasal passages for some reason. You might want to ask the vet.
5. You can prevent veggies going bad by thoroughly washing and drying them as soon as you bring them home, then wrapping them in paper towels and placing them in a non-airtight container. Place them in the vegetable drawer of your fridge.
It is recommended that you always spay female bunnies. In addition to often presenting aggressive behaviors, intact females have a 60-80% chance of developing often fatal reproductive cancers. This risk can be virtually eliminated by spaying. Fixed bunnies also have better litter box habits, can be bonded with other bunnies, and do not contribute to rabbit overpopulation. If you find a rabbit-savvy vet, the chance of death as a result of the surgery is much less than 1%.