Welcome!
I love piggies too! I had them growing up, but currently only have buns.
Your cage sounds great, I have a CC condo for my buns.
I tend to let my buns have free roam whenever I’m home and awake, which during the week is usually 4-6 hours per day, longer on the weekends.
Regarding spaying, female rabbits have high rates of reproductive cancers (estimates range from 50-75% depending on the age of the rabbit), and litter training can be hard without spaying, so it’s recommended. There is always a risk, as you know, but the surgery has gotten a lot safer as rabbit veterinary medicine has improved. The key is to find a good rabbit vet and make sure they do a lot of spays. You might reach out to local rescues and see what vets they recommend.
In terms of pellets, you can start scaling back. How much does she weigh? I give mine about 1/4 cup per day, split into two meals. Some people give even less than that if they have a dwarf breed.
For veggies, introduce slowly, 1 at a time per week to allow their system to adjust, especially if they’ve never had fresh foods. Cilantro is a good one to get them to try veggies since it smells so fragrant.
In general bunnies need more leafy greens than piggies. Things like carrot and bell pepper are more of a treat for bunnies.
The best way to help your bun bond with you is to play “hard to get”. Lay on the floor in their area, but ignore them. Read a book, watch tv, etc. But allow her to explore at her own pace and come to you. Hand feeding is also good (so you can hand feed pellets and treats). Don’t try to pet her or pick her up just yet. Once she starts exploring and will relax near you, then you can “ask” to pet her by placing your hand in front of her face on the ground. If she puts her head down, she wants you to pet her on the head.
What’s her name? Of course we all want pictures, of her and the piggies too! 
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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.