a) Who is it? Yes, this is fine.
I don't know who person's gender, name or both is at the door The meaning of this is obscure, and it lacks a full stop.
b) The baby is crying; please, take it. This is possible if you don't know the name or gender.
I know the baby's gender, but I don't know what the baby's name is; maybe I don't know either one.
2) I would like to know if this happens with animals too.
c) The dog is barking outside. It must be hungry. This is fine.
I think the word dog may be used as a neuter gender for referring a male (dog) or a female one (bitch), but I don't know what the dog's name is.
3) When an impersonal pronoun has a proper name, may be replaced by a personal pronoun?
d) Google translate should be sued for mistranslating the Gettysbug Address, she generates lots of money for paying a personal translator and saving the translation for a future use. I don't see the connection between the two parts of this sentence.