Only if you intend to get off the ship.
yes
No
Yes, you definitely need a passport to go to Honduras on a cruise ship. More particularly, you will need a passport to re-enter the United States.
No, you can visit Jamaica up to 90 days on your Italian passport.
Yes, you need a passport card to go to Jamaica. You can get these at any USPS and have your picture taken at drug stores.
If you're a US citizen and your cruise starts and returns to the same US port, you do not need a passport to cruise to the Bahamas.
yes you do need a passport throghout the cruise, especially to get out of the Bahamas visitor center,but when you go back on the cruise they will give you a carnival card.
yes
yes
no a passport
As you told that if you are living in Jamaica than there is no need of passport but if you belongs to other country than you have to take passport for going there. Yes you do need a passport to enter the country
you only need a passport if you are going to cruise to they place and fly back but it you were cruising from lets say Florida to the Bahama's and you don't stay in the Bahamas and cruise back then you don't need one