If they're nipping, they could be wanting your attention.
Or if it's painful then that generally means they don't like whatever it is you're doing to them or they don't want the attention. When they do this, make a loud squeak or sound (like EEK). Be consistent with it so they will eventually understand that they are hurting you. If that doesn't work, gently push their head to the ground with your hand and hold it there for a few seconds. This is how rabbit's scold each other.
Digging is a natural instinct. My rabbit LOVES to dig, especially at soft things like my blanket. I don't mind it as long as she's not ruining it which she hasn't. You can create a dig box for them so they can make better use of their energy on something else if it bothers you.