Answered by Shaykh Faraz Rabbani
In congregation after the Imam has finished reciting surah fatiha is one suppose to say “Ameen” out loud, say it quietly or not say it at all? What is the case for women in a mixed congregation (can they say it out loud)? What is the case when you’re having the congregation at home with one’s father, mother, brothers and sisters?

Walaikum assalam wa rahmatullah,
I pray that this finds you well, and in the best of health and spirits. May Allah grant you all good and success in this life and the next.
(1) The sunna is for the follower to say “Ameen” when the imam finishes their recitation of the Fatiha, for both men and women.
(2) In the Hanafi school, the proper way is to say “Ameen” quietly.
[ Shurunbulali, Maraqi al-Falah; Ibn Abidin, Radd al-Muhtar ]
And Allah alone gives success.
Faraz Rabbani