No, she has a green card. She was born in the Barbados.
I am an Irish Citizen and wish to become a Barbados citizen
If you are both United States citizens it is not illegal, wherever you are married.
To travel to Barbados, all one has to do is buy a plane ticket and fly to Barbados and meet all of the entry requirements. You are considered a tourist. To actually live in Barbados is a different story, and a completely different question.
A Barbadian.
No, as of current regulations, citizenship in Barbados cannot be obtained through a grandparent. Citizenship is primarily based on parental lineage or by birth in the country. You may explore other avenues, such as through investment or residency programs, to become a citizen of Barbados.
Yes they can live together
Australian female citizen marrying US male citizen - which would be easiest marrying in US and come back to Australia to live or marry in Australia to live?
Yes, but the US citizen should sponsor his/her spouse's immigration in order for him/her to get a green card.
Permanent resident can apply for US citizen after live in US for 5 years (continuously and not leave the US in the period of 5 years).
You can but be aware, that the UK citizen cannot legally change their status while in the US. It depends on where you both want to live. If the US citizen wants to come back to the UK, a marriage visa is needed from the British Embassy in the US. However if the UK citizen wants to live in the US, they will have to go back to the UK and the US citizen will then need to file the I-130. Until it comes through you cannot live in the US, but will have to wait in the UK.
NOPE