Why is the answer in English reverse than as presented? Shouldn't the correct order be "the girl and you"?
That is confusing, isn't it.
"The girl and you" was already accepted; I've now tried to make it the main translation.
The sequences αυ, ευ, ηυ are /av ev iv/, or /af ef if/ before a voiceless sound; the sequence ου is /u/; and otherwise υ is /i/.
(ηυ is rare, especially in modern Greek. I think it only occurs as the result of augment, which modern Greek usually doesn't do any more.)
εσύ is a pronoun, and those don't take articles -- as in English, where we do not say "the you".
Pronouns are definite by default; they refer to a specific person or to specific people, so you can't put "a" or "the" in front of them.
Just because it seems so uncoordinated, I have an impulse to write, "you and the girl." Does the word order matter? Could you swap it in Greek?
You may be confusing two things: words and things that the words stand for.
Girls are female.
The word κορίτσι is neuter.
The word refers to a girl, and girls are female, but the word is not feminine.
Word gender is more or less arbitrary. Things that refer to females need not be grammatically feminine, and vice versa.