Can You Offer Sujud As-Sahw in Sunnah Prayer?

Their imam forgot a prostration then he repeated the rak’ah, but some of them did not repeat it

He forgot the final tashahhud and said the salam

He did the first sajdah of sujood al-sahw (prostrations for forgetfulness in the prayer), then he remembered that he did not do anything that required sujood al-sahw

What is to be said in the prostration of forgetfulness and the prostration of recitation?

Should a latecomer count an extra rak’ah done with the imam?

Should he take his cue from the person next to him if he is unsure about the number of rak’ahs?

He forgot and said Allaahu akbar instead of Sami’aAllaahu liman hamidah

He said salaam before the end of the prayer by mistake then he started another prayer

The imam sat briefly after the third rak’ah and the people praying behind him alerted him to that; should he do the prostration of forgetfulness?