Who Are Munkar and Nakir?
Question

What is narrated about the questioning of the two angels Munkar and Nakir in the grave, and about their appearance? 
Is the hadith (narration) about them, in which the Prophet (peace and blessings of Allah be upon him) told ‘Umar ibn al-Khattab (may Allah be pleased with him) about them, sahih (authentic)?
Is it true that they drag their hair behind them and their eyes are like lightning and their voices like thunder and they strike the grave with their eye teeth and say: “Who is your Lord? What is your religion? And who is the Prophet who was sent amongst you?”
Praise be to Allah.What do Munkar and Nakir look like?
It is narrated in sahih reports that the two angels whose task it is to question the deceased are black and blue, and one is called al-Munkar and the other is called al-Nakir. 
Al-Tirmidhi narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “When the deceased – or one of you – is buried, there come to him two black and blue angels, one of whom is called al-Munkar and the other al-Nakir. They say: ‘What did you say about this man?’ and he says what he used to say: ‘He is the slave of Allah and His Messenger. I bear witness that there is no god but Allah and that Muhammad is His slave and Messenger.’ They say: ‘We knew that you would say that.’ Then his grave is made spacious for him, seventy cubits by seventy, and it is illuminated for him. Then it is said to him: ‘Sleep,’ and he says: ‘May I go back to my family and tell them?’ They say: ‘Sleep like the bridegroom who will be woken by none but the dearest of his family to him,’ until Allah raises him from that resting-place of his.” 
But if he is a hypocrite he says: ‘I heard the people saying something so I said something like what they said. I do not know.’ They say: ‘We knew that you would say that.’ Then it is said to the earth: ‘Squeeze him.’ So it squeezes him until his ribs interlock, and he will continue to be tormented therein until Allah raises him from that resting-place of his.” 
This hadith was classed as sound by al-Albani in Sahih al-Tirmidhi. 
Weak hadith about the description of Munkar and Nakir
With regard to the hadith of ‘Umar  (may Allah be pleased with him) to which you refer, it was narrated via weak chains of narration, such as the mursal (one whose chain stops before reaching the Companions) report narrated by ‘Abd al-Razzaq in his Musannaf from ‘Amr ibn Dinar, according to which the Prophet (peace and blessings of Allah be upon him) said to ‘Umar (may Allah be pleased with him): “How will you deal, O ‘Umar, with the two testers in the grave, when they come to you digging the earth with their eyeteeth, stepping on their hair (because it is so long), their eyes like dazzling lightning and their voices like deafening thunder, with a whip so heavy that if the whole world were to gather together to lift it, they would not be able?” ‘Umar (may Allah be pleased with him) said: “I will be as I am today”. He said: “As you are today?” He said: “Then I shall take care of them for you, in sha Allah.” 
Al-‘Iraqi said in Takhrij al-Ihya: 
“This was narrated like this, as a mursal report, by Ibn Abi’l-Dunya in Kitab al-Qubur, and its men are thiqat (trustworthy). Al-Bayhaqi said in al-I’tiqad: We have narrated it via a sahih isnad in a mursal report from ‘Ata ibn Yasar. 
I say: Ibn Battah narrated it in a mawsul report (reaching the Prophet) in al-Ibanah, from the hadith of Ibn ‘Abbas (may Allah be pleased with him), and it was narrated by al-Bayhaqi in al-I’tiqad from the hadith of ‘Umar (may Allah be pleased with him), but he said it is gharib (strange) with this isnad, which was narrated only by Mufaddal. Ahmad and Ibn Hibban also narrated from the hadith of ‘Abd-Allah ibn ‘Umar  (may Allah be pleased with him) that ‘Umar (may Allah be pleased with him) said: “Will our awareness be restored to us?” He said: “Yes, just as you are today.” ‘Umar (may Allah be pleased with him) said: “Then I will throw a stone in his mouth.” 
Professor Farij ibn Salih al-Bahlal said in his commentary on al-I’tiqad by al-Bayhaqi, after referring to the weak chain of narration: Perhaps by virtue of these isnads and corroborating reports its isnad may be hasan.” 
What are the 3 questions asked in the grave? 
The questions which the angels put to the deceased in his grave are: 

Who is your Lord? 
What is your religion? 
Who is this man who was sent among you? 

For more, please see these answers: 22203 , 43138 and 45325 . 
And Allah knows best.