谁的 + [noun]? [noun] + 是谁的?
The two orders differ only in emphasis. The second leaves 的 with no noun after it, which is normal: 谁的 on its own works like English "whose" without a noun.
The answer copies the shape of the question and usually drops the noun.
The 的 cannot drop, and the sentence takes no 吗, because 谁 already makes it a question.