We did the 4 night on the Wonder back in March. The pizzeria hours are 11:00am to 6:00pm. The dinners are considered “cruise casual” no shorts, t-shirts, open toed shoes but a suit and tie would be too much. The first night we saw people with shorts because of the luggage situation. I do not know about bringing your own drinks. We brought our on sport bottles for water on the excursions.
Nassau is Awesome and Castaway Cay is even more awesome. Have Fun!!!