Does the Imam say "Amen" during the Qunut supplication, or is saying "Amen" exclusive to the followers only? And does the Imam say "Amen" aloud, or is it exclusive to the followers, or do both the Imam and followers say "Amen" silently? And is invoking blessings upon the Prophet (peace be upon him) mentioned in the Qunut supplication?

The prescribed way for Qunut in Witr prayer is for the Imam to supplicate and the congregants to say "Ameen." The Imam should not say "Ameen" to his own supplication. The jurists have stipulated that the Qunut supplication should conclude with prayers upon the Prophet (peace be upon him), based on the saying of Umar: "Indeed, supplication is suspended between the heavens and the earth; nothing ascends from it until you send prayers upon your Prophet (peace be upon him)." The form of the Qunut supplication begins with the transmitted supplication and ends with prayers upon the Prophet and his family.