Purnama
Linguistically it derives from Sanskrit (purnima/purnama) but is widely used as a Malay/Indonesian name and thus considered Malay in contemporary onomastics.
The nearest Arabic semantic equivalent is البدر (al-badr), meaning 'the full moon.' Purnama itself is not Arabic.
Yes; Purnama is used by Muslim families in Southeast Asia. It is cultural and naturalistic rather than a scriptural name.
In Malay/Indonesian pronunciation: poor-NAH-mah, with even vowel sounds and stress on the second syllable.
Purnama is primarily feminine in regional usage, though lunar-themed elements can appear in compound names for any gender.