Zarqāʾ
No. Zarqāʾ is not mentioned in the Quran; its attestations come from classical Arabic literature and historical chronicles (e.g., the figure Zarqāʾ al-Yamāma in early Arabic sources).
The Arabic root ز-ر-ق (z-r-q) denotes the color blue; adjectival forms from this root describe blueness or blue-eyed features.
Yes. Zarqāʾ is a descriptive Arabic name with historical attestations; it does not invoke any prohibited meanings and is used as a personal name.
The name appears in early Arabic narratives and chronicles, most notably connected to the figure called Zarqāʾ al-Yamāma, known in Arabic historiography and literary tales.
A masculine adjectival form from the same root would be Azraq (أزرق), attested as an epithet; Zarqāʾ is specifically the feminine adjectival form and used as a feminine given name.