Nutmeg's got a great mommy!
Her cage looks great, with the exception of the Silent Spinner. Very glad you're already getting it replaced, the CSW is the absolute best wheel to replace it with.
Not active during the day is completely normal. Sometimes babies will get up during the day to eat more, and there's other cases where hedgies will get up in the day to be active for a little bit, but for the most part, they won't. They'll sleep all day and party all night.
She sounds like she's doing great for growing, and might turn out to be a bigger hog. Nothing wrong with that! She doesn't look pudgy or chubby at all to me, so I wouldn't worry much. What foods are in your mix? It does sound (to me) like she's eating a LOT, but she's also growing, and doesn't look overweight in the least, so I wouldn't stress about that either.
If you search through the Toys section, there's a LOT of ideas for basic toys, homemade toys, etc.
Yup, she may be starting her 12-week quilling, which would explain the quill loss. She could also have dry skin, if it looks really flaky and she's shedding a lot of skin flakes too. You can help with dry skin by putting flaxseed oil on her food, and also by including it in the rinse water after a bath. Oatmeal baths help with quilling as well - just get old-fashioned non-instant oatmeal, put a handful in a sock or nylon or something, and squish it in the water until it's cloudy. That'll help sooth and soften her skin and make her feel better.
Edit: I forgot to mention that that first picture is absolutely PRECIOUS and made me flail all over the place. <3