Mu'adh
Yes. Mu'adh ibn Jabal, a well-known companion (Sahabi) of the Prophet Muhammad, is documented in Hadith and early biographical literature; the name itself is classical Arabic.
Mu'adh comes from the Arabic root ع-و-ذ (ʿ-w-ḏ), which relates to seeking refuge or protection; the morphology produces the meaning 'one who is protected' or 'one who seeks refuge.'
Mu'adh is found in South Asia among Muslims, particularly in more traditional and religious naming patterns, though it is less common than some other classical Arabic names.
Yes. As with many Arabic names, Mu'adh can appear with honorifics or in compound forms (e.g., Mu'adhullah) though classical usage is typically the single name.
Historically and linguistically Mu'adh is a masculine name and is traditionally given to boys.