Carnival is deathly serious about the non-smoking policy. We've been three times on Paradise and have seen and heard of people put off for it- not just the smoker, but everyone in the party. You can purchase tobacco products in the cruise ports, but they must be turned over to Security at re-boarding. They will be kept for you and returned at debarkation in Miami.
There are two formal nights, Monday night and Friday night on the typical itinerary. A not insignificant people elect to go formal on formal night, meaning long gowns and tuxedos, although most do not. You would not be uncomfortable either way.
By the way, the photographers are great. Let them take as many pictures as you can stand. They are developed and displayed in a gallery, where you can pick and choose. The ones you don't want, you can literally drop into a trash can. No pressure whatsoever.
There is a waterslide at the main pool, and it gets lots of use, and not just from the kids.
Cat 4 and Cat 6 cabins are all approximately 185 square feet, which may not sound like a lot, but was just fine the two times we took our boys, and even better with just my wife and I. You can see pretty good pictures of both staterooms and public areas at Travelocity's site.
Hope you have a great time - we will be following you in September.