When I receive a group message in quick reply, would it be possible to have the group icon show as the contact’s image so I know that I’m replying to a group and not just that contact?
Additionally, if I touch the “open” button on a message that was sent to a group, it goes to messaging with that contact instead of the group chat.

Thanks!

If you receive an incoming QR message from a group (iMessage) then you will see a group chat icon. If not then either it’s not a group chat, or it’s not a group iMessage chat or there’s another MS app interfering on your device.