Is my prayer valid behind an imam who mispronounces Al-Fatiha in a way that changes the meaning, knowing that his prayer is invalid, and this is in a silent prayer?

Whoever's prayer is invalid due to a melodic error (laḥn) in Al-Fatihah that alters the meaning, then the prayer of anyone who follows him is also invalid. There is no difference between a silent and an audible prayer in this regard, because it is not permissible to follow someone who does not master Al-Fatihah, even in a silent prayer. This is because the Imam is in the position of bearing the recitation, and such a person is not fit for bearing.