Rifa'i
No. Rifa'i is a nisbah (attribution) historically linked to the Rifa'i Sufi order and to Ahmad al-Rifa'i; it is not a name that appears in the Qur'an.
It derives from the Arabic triliteral root r‑f‑ʿ (رفَع), associated with raising, elevation, or highness; the nisbah indicates relation to that root or to the place/lineage named Rifa'.
Yes, though it is uncommon. Using it as a given name often signals respect for the Rifa'i Sufi tradition or family ancestry that bears the nisbah.
Historically it has been used as a masculine nisbah; when used as a given name it is typically masculine.
Not inherently; it indicates affiliation or association with the Rifa' lineage or order. Any claim to authority would depend on family history or recognized scholarly standing, not the name alone.