Hürrem
No. Hürrem is Turkish in usage and derives from Persian khurram; it entered Ottoman Turkish through Persian influence rather than classical Arabic.
Yes. The best-known bearer is Hürrem Sultan (Roxelana), consort of Suleiman the Magnificent, attested in Ottoman chronicles and European sources.
No. The name is lexical (Persian origin) and is not mentioned in the Quran or canonical Hadith texts.
Khurram (خُرّام) in Persian means joyful, cheerful, joyful-prosperous and is the lexical source for the Turkish form Hürrem.
Hürrem is uncommon in contemporary naming but remains recognizable in Turkish and historical studies because of Hürrem Sultan; it is rarely used as a modern given name.