Welcome to the Cruise Reviews forum. No problem about posting under NCL...I can put a link to this thread in the Caribbean Port board if you'd like.
I haven't cruised at Christmas, but I have cruised NCL many times, most recently in 2010. Plenty of people dress up, as they do on other lines. I just got off a Holland America cruise and, other than formal nights, most people were in business casual. I didn't bring a gown with me on my NCL cruise, yet I did bring a couple of dressy tops and skirts for the Dress Up or Not Nights, when formal is optional. And, if you don't want to dress up, that's fine, too. On HAL last week, I had a simple black cocktail dress that I gussied up with a sheer shawl. I take this same outfit on NCL. Took up very little packing space.
You'll find a lot of opinions on whether it's preferable to book your shore excursions through the cruise line or go independently. My general rule is that I go with a ship excursion if (a) it's my first time visiting and/or (b) the places I want to visit are a distance from the port. In the case of the Mayan Ruins, the better ones are further from port... yet, I'll let the experts weigh in.