An interesting occurrence that took place today | A Fiqh lesson for us all

The incident (relayed to me by a brother): The imām added a third rak’ah in Fajr prayer today. When he stood up for the third rak’ah I said سبحان الله to alert him of his mistake but he continued on, so I remained seated until he completed the third rak'ah. I joined him in the final Tashahhud and ended my prayer with him. But I have two questions: 1. Were we supposed to follow him in the third rak’ah or remain seated as I did? 2. Someone joined the congregation during the second rak’ah and offered two units with the imām. Would this additional rak’ah count as a rak’ah for this person who joined in? What was he supposed to do in this case? ----------- I'll give you some time to think about the answers...