For
Castaway Cay, you probably don't need to reserve recreational equipment in advance -- I have rented bicycles and paddle boats while on the island with no problem. If you're sure that's what you want, it wouldn't hurt to reserve, but you may find enough to do that you don't need it, or may be affected by weather. If the ship can't disembark at all, your reservation will be refunded, but if the ship docks and the weather is cold, I think you'd still be charged.
The only excursion my family has done on Castaway Cay is the Stingray Adventure, which they enjoyed. We haven't been to Lookout Point.
In Nassau, we did the Greycliff chocolate-making tour, which was fun to do once. We went to Ardastra Gardens once, which was fun when the kids were young. We usually just walk around for a little while near the port or stay on the ship.
If someone in your family is interested in meeting the princesses, you should definitely try for the Royal Gathering when booking opens. There will be 4 or 5 princesses in the lobby, and guests go from one to the next getting photos and chatting. Some of the princesses may be greeting around the ship at other times during the cruise, but this would be a guaranteed time. If it's sold out when you try to book, you can ask at Guest Services once you're onboard to see if there have been cancellations.
I have not had issues with mosquitoes in Nassau or Castaway Cay, but repellent wouldn't hurt if you are concerned, especially if you're out late in the day.