Just because the head is engaged does not mean they can predict when you go into labor. My baby's head was engaged pretty early on and I went to 41 weeks. Babies are fickle like that.
The mucus plug is also normal. It's actually pretty nifty and can regenerate itself to some extent. The contractions could be braxton hicks. In fact, if they are irregular it is most likely BH.
So basically: have your bags packed and be prepared, but also be prepared to go over. When left alone, most first time moms actually go to an average of 10 days over. You never know though! Good luck :)