Is a latecomer who joins the congregation in the last rak'ah required to recite the final tashahhud and the Ibrahimiyyah prayer with them? And if he does so, is he then required to perform an intermediate tashahhud in the rak'ah that follows (which is the second for him)?

Whoever catches the fourth raka'ah with the Imam is required to sit for the final tashahhud, following the Imam. It is also recommended for him to agree with the Imam in the dhikr of the tashahhud, such as du'a, tahiyyat, and salat upon the family (of the Prophet). When he stands up after the Imam's salam to complete his prayer, he must sit for the first tashahhud, according to some scholars, and it is recommended according to others.