You got that right. All applications must be made through the mail. You could ask for an appointment but there are not that many if any available at any given time.
She doesn't have to put the Father down. Good job I insisted. It all depends on which Countries Automatically give Citizenship to the child through the mother not all Countries give it through a Father and I know this as it happened to me. Even though my name was on my Childs BC she never got UK citizenship and for that I am eternally grateful. The place is a cesspool. I would suggest that you do some research on it you will be very surprised.