Islamic Ruling on Talking During the Friday Khutbah and Saying Ameen
According to this Islamic ruling, speaking during the Friday khutbah is makruh and disliked, but saying Ameen softly to the khateeb’s dua is allowed. Raising the hands during the dua is also permissible.

Hazrat Abu Hurairah رضي الله عنه narrated that the Prophet ﷺ said that if you tell your companion to be quiet while the khutbah is being delivered, you have committed a useless act. This narration is recorded in Sahih al-Bukhari 934.
Based on this hadith, Islamic scholars have given the fatwa that talking during the Friday khutbah is disliked and makruh. Listening silently to the khutbah is recommended. However, speaking is allowed if there is a valid excuse.
Hazrat Anas رضي الله عنه reported that while the Prophet ﷺ was delivering the Friday khutbah, a Bedouin stood up and requested dua for rain because wealth was destroyed and children were hungry. The Prophet ﷺ raised his hands and made dua. This narration is also in Sahih al-Bukhari 933. This shows that speaking due to a need is permissible.
Islamic scholars also mention that when the khateeb makes dua, saying Ameen in a moderate voice is sunnah. Saying it loudly is not recommended because it may cause disturbance. There is no clear mention about raising hands specifically at this moment, but since raising hands in general duas is recommended, there is room to do so here as well.
This is the Islamic ruling and fatwa on this issue.