What does a worshipper recite in the third rak'ah of a silent congregational prayer (such as Dhuhr and Asr), if he caught the first two rak'ahs but thought they were the third and fourth, so he only recited Al-Fatihah in them? And in the third rak'ah, should he recite Al-Fatihah and a surah, or just Al-Fatihah? And is his prayer valid?

It is Sunnah for the worshipper (ma'mum) to recite a surah after Al-Fatihah in the first two rak'ahs. If the worshipper does not recite anything after Al-Fatihah (due to the imam bowing or for other reasons), nothing is incumbent upon him, because "the imam is a guarantor." In the last two rak'ahs, if the worshipper completes Al-Fatihah and the imam has not yet bowed, it is Sunnah for him to recite whatever is easy for him after Al-Fatihah and not remain idle, as this has been reported in the guidance of the Prophet (peace be upon him). However, if the imam bows quickly, the worshipper should bow with him, and he is not required to recite anything after Al-Fatihah. The prayer is valid in all the aforementioned situations.