Is the Prophet's saying, "Recite it to yourself," a definitive proof of the obligation for the worshiper behind the Imam to recite Surat Al-Fatiha silently even in loud prayers, and does "listening attentively" in the verse mean not moving the lips, or is it permissible to recite without disturbance?

The phrase "recite it inwardly to yourself" comes from Abu Hurairah and not from the Prophet, peace and blessings be upon him. The hadith does not clearly indicate the obligation for congregants to recite Al-Fatihah; it is possible that the intention is for the recitation of Al-Fatihah to be a pillar (rukn), but the congregant is exempted because the Imam's recitation suffices. Abu Hurairah's statement is general and does not specify whether it applies to loud or silent prayers. His command to recite could be due to its virtue, not its obligation. As for the verse: ﴿And when the Qur'an is recited, then listen to it and pay attention that you may receive mercy﴾, listening implies listening to everything that prevents one from hearing the recitation.