How is Surat Al-Fatihah to be recited in a loud congregational prayer if the worshipper joins the rak'ah before the Imam recites it, or while the Imam is reciting, and is it waived if he joins the Imam while he is bowing?

The preponderant and fatwa-sanctioned opinion is that Surah Al-Fatihah is a pillar (rukn) for the worshipper led in prayer (ma'mum), and it is permissible to recite it before the Imam begins it, and that does not cause any harm. In audible prayers, its recitation is prescribed either alongside the Imam's recitation, or after he finishes it if the Imam pauses afterwards. If you find the Imam in rukoo' (bowing), then you should bow, and the recitation of Al-Fatihah is waived for you. If you begin reciting Al-Fatihah and the Imam bows before you complete it, there are two views on the matter: either bow immediately in 따라 with the Imam, or complete Al-Fatihah and then bow, continuing the prayer with the Imam.