Mulhim
Yes. Mulhim is derived from the Arabic verb أَلْهَمَ (to inspire) and the noun إِلْهَام (inspiration); it functions as an active participle in Arabic morphology.
No specific form 'Mulhim' as a proper name does not occur in the Qur'an. The general concept of inspiration (ilhām) appears in Islamic discourse but not as this exact proper name in Qur'anic verses.
Yes. The lexical root and the notion of ilhām (spiritual inspiration) are important in Sufi literature; Mulhim is often chosen for its Sufi resonance as 'one who inspires' or 'the inspirer'.
Mulhim is rare as a contemporary given name; it occurs occasionally in literary or Sufi contexts rather than as a widespread popular name.
The related unisex noun Ilham (إِلْهَام) is used as a feminine or unisex given name; the active‑participle Mulhim is predominantly masculine in usage.