Moinuddin
Yes. Moinuddin is devotional in sense—it means 'helper/supporter of the faith' and has strong Sufi associations, notably with Moinuddin Chishti.
The root is ʿayn-waw-nun (ع و ن) giving Muʿīn (helper); combined with ad-Dīn (the faith) it yields Muʿīn al-Dīn.
Yes. The most prominent bearer is Moinuddin Chishti (Gharib Nawaz), a central Sufi saint in South Asia.
No. The exact compound 'Moinuddin' does not appear in the Quran as a proper name, although both components are standard Arabic vocabulary.
In Arabic script it is written as معين الدين or مُعِينُ الدِّين; in Urdu commonly as 'معین الدین' or 'مُعینُ الدِّین'.