They are different:Marriage register would be the system of keeping tract of marriages in a certain jurisdiction.Register marriage would be the act of registering a marriage in the local marriage register.
The easiest way is to register your marriage with the nearest US embassy or Consulate in the country where you marriage took place and from there, the consulate will be able to further advice ..I am assuming that you the US Citizen is based overseas right ?
Some US states and foreign countries have laws permitting same-sex marriage. Some US states and foreign countries have laws prohibiting same-sex marriage.
Yes. Your foreign marriage is legal in the United States.
Why would you register it? It is valid in both countries. Your marriage certificate would be recognized as valid if you needed proof.
yes
There is no registration requirement in USA. You just use your original certificate from your country in all application procedures.
You better register the marriage at the nearest US mission in the country where you are getting married to avoid the risk that the US government may not recognize marriage certificate from that specific country.
It shouldn't. Ask about it.
Most foreign marriages are considered legal in the US. There are exceptions, so if you got married outside the US, you may want to consult an attorney to either confirm you are not one of those cases, or to find out how to get your "foreign" marriage legally recognized by the US. An example where a foreign marriage would not be considered legal in the US is if a same-sex couple entered into a union in a country that recognizes same-sex unions and then moved to a state in the US that explicitly bans recognition of such unions.
Yes provided the couple can submit the marriage certificate and also register the same in US. Subsequently the wife can change name and update it on relevant documents based on proof of marriage.
No. A matricula consular proves that you are a citizen of a foreign country.