"This/that" are demonstrative pronouns and can be used in the place of personal pronouns to identify a person, an object or something abstract. "This" points to something which is closer in proximity or time, while "that" points to something which is further away.
"Is this your doctor?"
Indicates a very close proximity. Imagine holding something in your hand, or holding someone by your hand. If you were holding up a photo of the doctor, you could say "Is this your doctor?"
fx. "Is this your son?" - indicates that you are holding the son by your hand, while adressing the parent
"Is that your doctor?"
Indicates a distance between you and the doctor. Imagine pointing at someone/something.
fx. "Is that your son?" - pointing at the son from a distance
"Is s/he your doctor?"
Can be used in the same way as "That", for instance while pointing, but to specify the gender.
Can also be used to refer to a previously mentioned person.
fx. "I met Linda Hunter today. Is she your doctor?"
As for the answers, "it" does not sound right when referring to a person.
- "Is that your doctor?"
- "Yes." or "Yes, that´s my doctor." or "Yes, that´s correct."
- "Is this your son?"
- "Yes, that´s my son"
Notice the difference here, because the parent is not as close to the "son" as the person asking.