I would say that it appeared that formal nights begin at first seating. They continue for the whole evening, even late seating and afterwards. Formal wear is what they mean about formal nights, AND even then it is NOT required. There will be a photographer with some really nice back drops for great "take home" shots of yourselves infront of the ship, etc. I refuse to wear a tux or suit and tie since I'm on vacation, and have had no problems with ship's people asking me to change cloths.
"Beach" on the ship are in each cabin for you to use, and they can be exchanged on the pool decks whenever you like. HOWEVER, if you loose one, last time I heard that they charge yiour sea pass card $20. I personally have never bought a $20 towel anywhere, so I'm not about to do so on a ship.
You're gonna LOVE cruseing!