For me, the only natural answer is 3 Is that your mother? Yes, it is. The 'it' refers to the demonstrative pronoun 'that' , and has nothing to do with the gender of the person referred to. Is that your teacher? Yes, it is. Is that the President? Yes it is. But Is she your mother? Yes, she is. In my view, 'Yes, that is' would be a very unnatural way to answer.

um... I would probably say "Yes, that's my mom", as we used "that" in the question.

The most natural and correct answer is, number 2. Since we used "that" to refer to your mother we should also use the same word to refer to her again. If we asked "Is she your mother?" We should use the pronoun "she" to refer to her again. It's the same situation for "it." But it would be rude to refer to a person as "it."

I would say "Yes, that's her." which is the most natural sounding and is most like #2. Now that you have drawn attention to something (in this case the person's mother) using "that," you would now refer to her as "she."