Is it legislated to recite Al-Fatihah or the opening supplication (Du'a al-Istiftah) when entering into prayer shortly before bowing (Ruku'), and what should the follower (Ma'mum) do if the Imam bows before he completes Al-Fatihah?

Reciting the opening supplication (Istiftah) is a Sunnah (definition). Reciting Al-Fatiha is obligatory for the follower, according to the soundest opinion. If the follower fears missing Al-Fatiha, he should start with it. If the Imam bows before the follower completes it, the follower should bow with him, and the remainder of Al-Fatiha is waived for him, based on the Prophet's (peace and blessings be upon him) saying: "Indeed, the Imam is appointed to be followed, so do not differ from him. When he says 'Allahu Akbar', then say 'Allahu Akbar'. When he bows, then bow."