What is the ruling on raising one's hands and raising one's voice with "Ameen" behind the Imam when seeking aid during the Friday prayer (Salat al-Jumu'ah), and is it permissible to raise one's hands when passing by a verse of punishment or mercy, whether one is praying alone or with family, and what should the Imam and congregants do in this situation?

The scholars have explicitly stated that it is disliked for the khatib (preacher) to raise his hands in dua' (supplication) during the khutbah (sermon). As for the ma'mum (follower), there is a difference of opinion. Saying ameen to the khatib's dua' is encouraged silently. As for supplicating upon passing by a verse of mercy and seeking refuge upon passing by a verse of punishment, both inside and outside of prayer, it is legislated. It is recommended for the imam (leader), the ma'mum, and the individual worshipper to do so. There is no harm in raising one's voice to an extent that those nearby can hear, but the ma'mum should agree with what the imam says and not say ameen to his personal dua'. As for raising hands in dua' during prayer, it is only transmitted in the qunut (supplication during prayer). Apart from that, hands are not to be raised by the imam, the ma'mum, or the individual worshipper. However, outside of prayer, there is no harm in the reciter or the listener raising their hands.