Is the worshiper required to recite the opening supplication (Du'a al-Istiftah) and Al-Fatiha if he catches the Imam in the first rak'ah after Al-Fatiha, or should he listen to the Imam's recitation, and what should he do in a silent prayer?

If the Imam begins reciting in a loud prayer, it is best for the worshiper to listen, unless he cannot hear the Imam's recitation, in which case there is no harm in saying the opening supplication (Istiftah). In a silent prayer, it is permissible for the worshiper to say the opening supplication. However, if the worshiper fears that he will not be able to recite Al-Fatihah before the Imam bows, he should begin reciting Al-Fatihah and not say the opening supplication, because Al-Fatihah is obligatory (fard) and the opening supplication is a sunnah. This is the established ruling.