For all the weather stats about Grand Cayman (or any other destination for that matter) you could ever want go to:
www.wunderground.comUsing the "Travel & Activities" dropdown link select "Travel Planner". Enter the airport code for Grand Cayman (GCM) and your planned dates of travel. You'll be directed to all sorts of weather data including a chart showing what the actual weather was on the island for every day during that period over the last 10 years. Study the material and you'll now more about Grand Cayman weather than most locals.
You might want to go to the main list of Traveltalk Forums and select the Cayman Island Forum for answers to your other questions (you've posted this question on the "General Caribbean Forum).