Mehrshad
Yes. Mehrshad is Persian in origin and used within Persian-speaking Muslim communities; it combines Persian lexical elements rather than Arabic religious terms.
'Mehr' can denote sun, affection, kindness, or be tied to the ancient concept of covenant; it is a common element in Persian names.
Compounds using Mehr- and -shad appear in Persian anthroponymy and literary use; Mehrshad is historically plausible and attested in regional records though relatively rare.
No. Mehrshad is Persian in origin and does not derive from Quranic Arabic; it is cultural-linguistic rather than scriptural.
Diminutives may include 'Mehr' or 'Shad' depending on family practice; Persian nicknaming is flexible.