What should one do who entered the prayer and caught the last rak'ah, and recited Al-Fatihah and a surah, then the imam said the taslim while he did not know it was the last rak'ah; should he cut off the prayer and repeat it, or complete the remaining rak'ahs?

The latecomer (masbuq) must complete his prayer after the Imam's tasleem. It does not matter if he does not know the rak'ah in which he joined the Imam. He should complete the remaining rak'ahs and recite the tashahhud at the second. It is permissible for the latecomer to recite a surah with Al-Fatiha in the rak'ah in which he joined the Imam, as well as in the second rak'ah (for the latecomer). As for the remaining rak'ahs, they should be with Al-Fatiha only, or he may recite a surah in the second and third rak'ahs and Al-Fatiha in the last. There is a difference of opinion on this matter.