Zulaykha
No. The Qurʾān narrates the episode involving Joseph and the wife of al-ʿAzīz but does not record her personal name; the name Zulaykha appears in tafsīr and later Persian and Arabic literary tradition.
It conveys beauty and brilliance; in the literary tradition it has the connotation of luminous attractiveness. The exact etymology is via later Persian and Arabic usage rather than a single classical root in the Qurʾān.
Yes. It is a classical literary name used in Muslim cultures. As with any name, families choose it with awareness of the story and its moral context in Islamic literature.
Zulaykha appears in medieval Persian, Ottoman and South Asian literary works, tafsīr commentary, and later poetry and prose traditions; it has been used historically in those cultural spheres.
No standard male form exists; the name is specifically feminine in the literary-historical record.