Was Diba'ah bint Al-Zubair circumambulating naked, and would all Arabs sing similarly before the Prophet forbade that? And what is the authenticity of the Prophet's marriage to her and the story of her going out for Hajj, and did he say to her: "Perform Hajj and stipulate that your place is where you are detained"?

Ḍubāʿah bint al-Zubayr was the Prophet's paternal cousin, not one of his wives. Neither she nor any woman from Quraysh circumambulated the Kaaba naked. As for Ḍubāʿah whom the Prophet intended to marry, she was Ḍubāʿah bint ʿĀmir, but the Prophet did not marry her, and the story has a weak chain of transmission. Some Arabs used to circumambulate naked in the pre-Islamic era (Jahiliyyah), but Islam prohibited this, and the verse: "O Children of Adam! Take your adornment at every masjid" was revealed for this very reason.