The English translation for the Spanish phrase luna nueva is new moon. It can refer to the actual new moon which is the first phase of the moon or it could refer to something else.
dirección nueva
"Buena suerte en la tienda nueva."
la vida nueva
That can be translated as "vida nueva".
You have given an English phrase, "new life," but it is not clear what language uyou want to translate it into. Some possibilities: vida nueva (Spanish) nova vita (Latin) nouvelle vie (French) neues Leben (German)
Loose translation: "What's new".
Translation: Desastres naturales en Nueva York
Buena suerte en la nueva tienda.
NTV Nueva Traduccion Vivi-ente.. its the NLT (new Living Translation) in spanish.
It means "new life" source: I am in Spanish class
New York is a proper noun so it's still pronounced New York in Spanish. Also some say Nueva York.
"Mi nueva casa" means "my new house" in English. It is a phrase used to refer to a recently acquired or moved into place to live.