düşman-ı in this case represents the possessive pronoun rather than converting düşman into a direct object, doesn't it?
yes, literally it means "her/his enemy does not exist"
Can this not have a pronoun?
O düşmanları yok
If you were to have a pronoun, you would have to use "onun" because of the possessive construction in the sentence. "onun" in this sentence means "she" in the English translation :)