Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Dear brother!
Here are answers to your questions:
1) As for the Surah that tells nearness of the Prophet's (Sallallahu Alaihi wa Sallam) death, it is Surat An-Nasr (victory). It is recorded by Imam Ahmad and others from Ibn 'Abbas who said that when Surat An-Nasr was revealed, Allah's Messenger (Sallallahu Alaihi wa Sallam) said: "My death has been announced" .
2) Surat Al-Ma'idah (the table) was the last Surah to be revealed. Jubair Ibn Nufair said: "I performed Hajj, and then I came into 'Ayisha (Radiya Allahu Anha) who asked me: O Jubair ! Do you read Al-Ma'idah? I said: Yes. She said: It was the last revealed Surah. So, follow what you find in it concerning Halal and avoid what you find in it concerning Haram" . [ Ahmad ].
This means that it was revealed after Surah An-Nasr.
3) The last verse that was revealed before the death of Prophet Muhammad (Sallallahu Alaihi wa Sallam) was {And be afraid of the Day when you shall be brought back to Allâh. …} [2: 281].
This issue is proved from Ibn Abu Hatim 's narration that reads: "The Prophet (Sallallahu Alaihi wa Sallam) lived only for nine nights after revelation of these (above-mentioned) verses, and he died on Monday, the 2nd night of Rabi'" .
Allah knows best.