Can I put a nightlight in the nursery?

Yes. Sure! a gentle nightlight is just fine so that your baby can be aware of his surroundings when he wakes up at night. Some babies like this very much. If your baby seems to prefer it dark, that's ok too!
Yes. Absolutely. Babies sleep better in the dark, just like adults, but having a dim nightlight in the nursery is fine. It will also help you see a little better during those late night diaper changes.