No. You do not need a passport since St. Thomas is part of the U.S. Virgin Islands, which is considered U.S. Territory. If you wanted to venture to the British Virgin Islands (B.V.I.) a passport is required.
Yes! Humidity is usually between 90-100% and average annual temperature is around 80 degrees.
Cyril E King-Airport in St. Thomas U.S.V.I. - Airport code: STT
Depending entirely on where you stay, you may not need a car. If you are near any main road on St. Thomas you can easily grab a Safari a.k.a. "The Dollar Holler". These are the local transport "system". There is no set schedule but you usually never wait longer than 10 minutes, depending on your area. They are between $1-$4 per person. Traveling to and from the airport there are no Safari's. Cab fares can range from $10-$25 per person, each way.
You can rent or buy anything you might need or want for a very good deal. Dive kit rentals are around $25/day, and snorkel sets $10/day. If you wanted to buy gear here as a souvenir the brands available on island are excellent and prices reasonable. EXCEPT if you need prescription lensed mask or reader inserts, definitely bring those with you. Check out links below to see how to get underwater: https://www.cokidive.com/ http://www.redhookdivecenter.com/
If you have AT&T, then YES!! If you have Sprint or Verizon....possibly. The service for Verizon and Sprint is a bit more scarce than AT&T, but not absent. You will NOT need to change any part of your plan in order to use your phone here.