Mujahid
Yes. Mujahid is historically attested; a prominent early scholar with this name is Mujāhid ibn Jabr, a noted Qur'ānic exegete quoted by later authorities.
The precise proper name 'Mujahid' does not appear as a personal name in the Qur'an, though the verbal and nominal forms of the root j‑h‑d (to strive) occur in Qur'anic discussions of striving and effort.
Mujahid (مجاهد) is an active participle meaning 'one who strives'; Jihad (جهاد) denotes the concept 'striving' itself. Both derive from the same root but serve different grammatical roles.
Yes. It is used historically and in modern times; families who choose it often emphasize spiritual striving, devotion, or remembrance of early scholars. Sensitivity to local cultural perceptions is advised.
The corresponding feminine form would be Mujahida (مجَهِدَة/مجاہِدَة) in Arabic morphology, but its usage is less common and depends on regional naming practices.