Qutayba
The Umayyad general Qutayba ibn Muslim (d. 715 CE) is the most notable historical bearer; he is widely mentioned in early Islamic chronicles for his campaigns in Transoxiana.
Qutayba follows Arabic diminutive morphology; it is a proper name formed in a diminutive pattern rather than a descriptive adjective.
No. Qutayba is a historical personal name attested in chronicles and biographical literature, not in the Qur'an.
Yes, though it is rare today. It is recognized as a classical name with clear historical precedent but is uncommon in contemporary naming practice.
It is attested in early Arabic/Umayyad historical records and therefore associated with the classical Arabic-speaking Islamic milieu of the 7th–8th centuries.