buy an underwater camera for your excursions. Leave the digital/video camera locked in your safe in your stateroom.
Channunkaab National Park - yes they have lockers, and you can purchase a video of your dolphin swim.
Most folks just wear their bathingsuits under a pair of shorts and a t-shirt. Make sure you have a good waterproof sunscreen. If you have your own snorkel gear, bring it along. The Sting Ray excursions provide snorkel gear. If you want to snorkel after your dolphin swim you will have to rent it either on the ship or at the park.
Formal night is Usually the night of your first full day at sea.
Don't bring a lot of cash on your excursions, just enough for cab fare, tip, food and small souveniors. For large ticket items use your credit card.