My baby is constantly nursing. Is this normal?

Yes. This is normal. Most of this is likely true feeding and necessary but some babies will use breastfeeding s a pacifier. Essentially true feeding is vigorous and consistent. Suck, suck, breath... Pacifying feeding is 30-40 minutes later and more like suck, snooooooooze, suck, snoooooze. During this phase of feeding baby isnt eating, just pacifying. That feeding can be stopped.
Yes. Just means your patient is hungry and/or desires attention. Check with your ob/gyn doc if this is a problem.