Would fata here mean girlfriend or daughter?
We don't really use "fată" for girlfriend; that and the use of the plural/politeness pronoun, strongly indicate that "daughter" is what is meant here. Though the English translation seems to suggest a "girlfriend".
OK, thanks! And in that case, how would you say "girlfriend"?
"prietena" which is the feminine form of "friend"
The "mireasă/mire" maybe it would be the literal translations of girlfriend/boyfriend?
That means bride/groom. Asta-i altă mâncare de pește ;D
would "ea este fata voastra" be correct as well?
Yes, because "e" is the short, informal version of "este."