I want to know about Prophet Muhammad's life. Please tell me about the last Salat performed by the Prophet and the Surah which He recited in it.
There's a hadith in sahih al-Bukhari suggesting that the last prayer the prophet () lead in a his mosque was a maghrib prayer and he recited in it surat al-Mursalat.
I heard the Prophet (ﷺ) reciting Surat-al-Mursalat `Urfan (77) in the Maghrib prayer, and after that prayer he did not lead us in any prayer till he died. (Sahih al-Bukhari)
There are no details on how he recited it (did he split it or recite it twice or recited a different surah too).
But he entered the mosque on the day he died (a Monday) to see/witness the congregation prayer lead by abu Bakr:
While the Muslims were offering the Fajr prayer on Monday and Abu Bakr was leading them in prayer, suddenly Allah's Messenger (ﷺ) lifted the curtain of `Aisha's dwelling and looked at them while they were in the rows of the prayers and smiled. Abu Bakr retreated to join the row, thinking that Allah's Apostle wanted to come out for the prayer. The Muslims were about to be put to trial in their prayer (i.e. were about to give up praying) because of being overjoyed at seeing Allah's Messenger (ﷺ). But Allah's Apostle beckoned them with his hand to complete their prayer and then entered the dwelling and let fall the curtain. (Sahih al-Bukhari)
While Abu Bakr was leading the people in the morning prayer on a Monday, the Prophet (ﷺ) came towards them suddenly having lifted the curtain of 'Aisha's house, and looked at them as they were standing in rows and smiled. Abu Bakr tried to come back thinking that Allah's Apostle wanted to come out for the prayer. The attention of the Muslims was diverted from the prayer because they were delighted to see the Prophet. The Prophet (ﷺ) waved his hand to them to complete their prayer, then he went back into the room and let down the curtain. The Prophet expired on that very day.
I couldn't find any source quoting what abu Bakr actually recited. At this point the prophet () has not lead a prayer in the mosque for several days due to his illness.
As Medi Saif pointed out, Prophet (peace be upon him) did not pray in the mosque for some time and he appointed Abu-Baker Assidiq to lead the prayer, a total of 17 prayers. Which suggests that the Prophet (peace be upon him) did not go to the mosque for at least 3 days. According to the Muslim historians and hadith scholars, As-sayuti, An-nassaiy and Ibn-Katheer, Mohammed (peace be upon him) went to the mosque on Monday, the day he died, and prayed Morning prayer (sitting) behind Abu-Baker Assidiq. This was his last prayer. There was no mention of the suras which Abu-Bakir read.