Is it permissible for a woman to recite the Quran in a silent prayer or in normal recitation without moving her lips, and is it obligatory for a man to only hear himself in congregational prayer?

Reciting Surah Al-Fatihah is obligatory in both audible and silent prayers. It is a pillar according to the majority of scholars, based on the Prophet’s (peace be upon him) saying: "There is no prayer for one who does not recite the Opening of the Book (Al-Fatihah)." As for someone praying behind an Imam, they should recite Al-Fatihah if they do not hear the Imam's recitation. If they hear it, their obligation is to listen attentively, because the Imam's recitation is considered a recitation for them. It is waived for the latecomer (masbuq) who does not catch the recitation. Regarding silent recitation, it is necessary to move the tongue and lips, which is the minimum level of whispering. The Imam in an audible prayer should hear himself and those immediately beside him, which is the lowest level of audibility.