No. You need your US passport.
does a citizen of Mexico need a passport to go from the us to Mexico and back? He is legal to be in us but not a us citizen.
If you are a US citizen, and the cruise ship departs and returns to the same US port, you will not need a passport to go on the cruise - as long as the cruise ship does not stop in any countries that require a passport for US citizens. If the ship is only cruising in Mexico, and returns to the same port from which it departed, you can board the ship with a certified copy of your birth certificate and a government issued photo id. It is much better, however, to have a passport. If, for example, there is an emergency and you have to leave the ship and fly home from Mexico, you will need a passport.
Yes.
it would go to the legal resident of the host country
No not if your a United States citizen.
Yes, he does.
If you are US, Canadian or European citizen you can enter Mexico without the need of a visa.
Right.
No.
Not any quicker than if you hadn't. However, your children will be citizens.
I am not sure about the UK but to Mexico the children have to have both parents consent to fly into and from Mexico.. My husband also had to go to the visa office and sign a papper giving his permission.. Hope this helps some..
no not to the carabean but can go on cruise ship just might not be able to get off at port.