Is it normal to have regular labor contractions (about every 10 minutes) at night, but that will then go away in the morning?

Very normal: As long as you are near term, that's normal. Women can have nightly episodes of "false labor" for days or even weeks prior to the big day. It's your body's way of warming up for the event. We usually ask women to wait until contractions are 4-5 minutes apart, last about a minute, and persist in that pattern for an hour or two, prior to heading to the hospital. Good luck!