What is the ruling on praying behind people of innovation, and is it permissible to say "Ameen" aloud after Al-Fatiha when the Imam does not say "Ameen"?

Prayer is not valid behind an innovator whose innovation reaches the level of disbelief (kufr). As for the transgressor (fasiq) and the innovator whose innovation does not reach the level of disbelief, prayer behind them is valid. Some scholars dislike praying behind them for the sake of enjoining good and forbidding evil, especially if there is a benefit in boycotting them until they repent or are removed. However, if abandoning prayer behind them leads to missing the Friday prayer and congregational prayer, then one should not abandon praying behind them, and praying behind them is preferable to praying alone. As for saying "Ameen" aloud, it is a Sunnah and not obligatory, and the prayer is not invalidated by omitting it. Saying it silently is the view of Abu Hanifa and a narration from Malik.