Muzammil
Yes. The vocative يَا أَيُّهَا الْمُزَّمِّلُ appears in Surah Al-Muzammil (73:1); the term is used as a title/epithet.
It is an intensive participle meaning 'the wrapped one' or 'the enshrouded one,' from the Arabic root ز-م-ل.
It is attested and used but remains comparatively rare; it is chosen by families seeking a Quranic and classical Arabic name.
Yes. Because it appears in the Qur'an and evokes prophetic devotion, it carries pious and devotional connotations.
There is no standard feminine classical form; Muzammil is conventionally a masculine name.