"Are you this girl?"
Translation:Bist du dieses Mädchen?
"dies" is only a fancy version of "das" but rarely used. as for "dieses":
der Hund / die Katze / das Haustier // the dog, cat, pet
dieser Hund / diese Katze / dieses Haustier // this dog, cat, pet
Die Mädchen is plural and refers to more than one girl. Das Mädchen is singular and refers to one girl. So "das Mädchen" becomes "dieses Mädchen".
But this is asking about one girl, not more than one. So if it's based on plurality, I still don't understand.
We only know for sure that it's asking about one girl because of the "-es" conjugation on "dieses." If it were "diese Mädchen," it would be asking about multiple girls. (Which is less likely in this sentence, but perhaps the speaker is, e.g., pointing out multiple photos and asking if all those photos are of that person.)
Dies is a neutral demonstrative pronoun. It is never used in combination with the nuon it refers to (not: dies Fahrrad, but dieses Fahrrad), and it is mostly used to refer to facts, to previous sentences for example, or if you point to things (Dies ist ein Fahrrad). And it's more written language. Dies war das Wort zum Sonntag ;-). Dies ist alles, was ich dazu sagen kann :-).
Right, you need an ending if "dies-" is right before a noun. So "Dies ist ein Mädchen" but "Bist du dieses Mädchen."
No, then "dieses" would have to be conjugated as plural and be "diese Mädchen." (Note that "Mädchen" is both the singular and plural form; we can only distinguish them by the conjugation of "diese/dieses.")