1. You are never "out" of milk. Your body is always making more. I would not give formula. She was probably just cluster feeding, which is really normal.
2. Why didn't you just put her to bed at 6? Sounds like she was ready. It is normal for newborns/infants to have early bed times.
3. Is the nap nanny safe for sleeping? I don't have one and don't know what the company says. I would not worry about a newborn sleeping in her crib. It's not a big deal. Imagine what it's like for her - she's so tiny, used to be warm and cuddled and cozy - the crib is big, flat and not cozy. My daughter slept swaddled in her swing or bouncy seat for most of her 9 months and sleeps fine in a crib now. I didn't like crib wedges myself.