The problem with C is that there's so much distance between the possessive adjective "whose" and the noun it's defining ("dress.") The previous answers seem to indicate that it might sound okay in British English, but in American English it would be an extremely formal and awkward-sounding construction. The only problem with A and B is that the answer is too long to be a natural match for the questions. Natives wouldn't normally repeat so much information from the question in their response. For A and B, more natural answers would be much shorter-- like, "Yes, it is." or just simply, "Yes."

Dan is correct. Those are four good sentences. However, assuming the question was to state which of the four questions could have "It is my mother's dress" as its answer, it would still be true that all four would be correct. C and D would be better answers than A and B (because there is no need to say "mother" twice) but A and B are not wrong. As for C and D, both are gorgeous and neither has any advantage over the other. "Whose is this dress?" is extremely common. Nothing would be gained by bringing the words "whose" and "dress" closer together because "whose" does not modify "dress". Rather, "whose" acts as a pronoun. When used as a pronoun, "whose" can be VERY far from whatever it refers to: "We saw a lost puppy while we were walking home and nobody knew WHOSE it was".

Both C and D are correct...

All four questions are fine. A and B and C and D. Nothing wrong with any of them. Or, is there a question or instruction you're not telling us?

Yes, C and D both work. The only difference is is that in C the speaker is presumably holding the dress, and in D, pointing to it further away, but the answer 'It is my mother's dress' applies equally well to both. I actually couldn't hazard a guess as to which they consider 'more correct'.