Do fallen angels know and understand the Bible according to the Calvinist?

The devil knows the Bible like he demonstrated in the tempation of Jesus. He did it by quoting verses of the OT in Matthew 4:1-11 but He do not understand the Bible. In Matthew 8:28-34 the demons knew there is a judgment and a comming of Jesus, but they do not understand that must be an atonement of sins first.

According to calvinism TULIP is a summary of their doctrine which comes from a correct interpretation of the Bible, if the devil doesn't understand the Bible, he won't understand TULIP

The devil believes in Total Depravity, the T in Tulip. This he states in the Book of Job directly, as well as through his influence upon Eliphaz through the sending of an evil spirit in a dream.

‘Can a mortal be more righteous than God?
    Can even a strong man be more pure than his Maker?
18 If God places no trust in his servants,
    if he charges his angels with error,
19 how much more those who live in houses of clay,
    whose foundations are in the dust,
    who are crushed more readily than a moth!
20 Between dawn and dusk they are broken to pieces;
    unnoticed, they perish forever.
21 Are not the cords of their tent pulled up,
    so that they die without wisdom?’  (Job 4:17-21)

The devil denies the Perseverance of the Saints (the P in TULIP), insisting that Job will curse God and die (Job 1 & 2). Job does not do that. Did that persuade Satan, or did he merely consider Job an exception to the rule? That is unclear.

The reason that Satan denies perseverance is that he only admits to the existence of a materialistic grace, not an Irresistible Grace (the "I in TULIP). Satan insists that if the material blessings of the Hedge around Job (a symptom of the true grace) are withdrawn, that Job would abandon his faith. Clearly, what held onto Job was more than selfish greed for material possessions.

However, these are Satan's arguments. The very substance of his attack on Job exhibits an understanding of God's plan. To storm a castle, you need to study the fortifications so that you can breach them. Satan launches a frontal attack on all God's truths so as to shake Job free of the Lord's grasp. The very comprehensive nature of that attack suggests that whether he believes God's doctrines or not, he knows them well enough to structure his temptations, persecutions and the like.

As for the remaining letter, U, Unconditional Election, Satan induced the friends to convince Job that God had abandoned him and would not take him back, or listen to his prayers, or regard his piety. He tried to convince Job that he was not hearing special wisdom from God. For example:

Do you listen in on God’s council?
    Do you have a monopoly on wisdom?
What do you know that we do not know?
    What insights do you have that we do not have? (Job 15:8-9)

Satan tried to prove to Job that God had not chosen him.

To sum up, I believe Satan knows the essentials of TULIP insofar as proving it false is priority for him. If he didn't know it, he couldn't be such an effective adversary.

This question is incredibly broad, However there is some biblical evidence which can be brought to bear on the situation.

In the 12th chapter of Revelation we are told

7 And war broke out in heaven: Michael and his angels fought with the dragon; and the dragon and his angels fought, 8 but they [a]did not prevail, nor was a place found for [b]them in heaven any longer. 9 So the great dragon was cast out, that serpent of old, called the Devil and Satan, who deceives the whole world; he was cast to the earth, and his angels were cast out with him. 10 Then I heard a loud voice saying in heaven, “Now salvation, and strength, and the kingdom of our God, and the power of His Christ have come, for the accuser of our brethren, who accused them before our God day and night, has been cast down. 11 And they overcame him by the blood of the Lamb and by the word of their testimony, and they did not love their lives to the death. 12 Therefore rejoice, O heavens, and you who dwell in them! Woe to the inhabitants of the earth and the sea! For the devil has come down to you, having great wrath, because he knows that he has a short time.”

This implies that at least one of fallen angels, Satan, has some insight into prophetic events.

Now we look to the Lord Jesus and his interaction with Satan in the wilderness in Luke 4:9-11

9 Then he brought Him to Jerusalem, set Him on the pinnacle of the temple, and said to Him, “If You are the Son of God, throw Yourself down from here. 10 For it is written: ‘He shall give His angels charge over you, To keep you,’ 11 and, ‘In their hands they shall bear you up, Lest you dash your foot against a stone.’ ”

Here the devil quotes a few old testament scriptures, rightly attributing them to the Christ. This implies that the devil was familiar with the scriptures existing up to that point.

Also in matt 8:28-29 we see a demon who is also familiar with future prophetic events

28 When He had come to the other side, to the country of the [c]Gergesenes, there met Him two demon-possessed men, coming out of the tombs, exceedingly fierce, so that no one could pass that way. 29 And suddenly they cried out, saying, “What have we to do with You, Jesus, You Son of God? Have You come here to torment us before the time?”

Notice that the demon does not rightly divine Jesus Christ in his mission to be a savior to the world (john 3:17). But he does anticipate a final judgement of evil.

I hope this is informative to you. Whether or not the demons affirm TULIP, i'm afraid is beyond the information available in the scriptures. ( At least to my imperfect understanding)