Relationship to the New Testament
Daniel's visions are obviously reflected to some extent in the New Testament, but I disagree with how the New Testament usage of Daniel is meant to be interpreted.
The Beast of the Revelation
John rather clearly makes a connection between the Beast of the Revelation with the 'dread beast' of Daniel 7. But that is not where John stops. He also clearly makes a connection between the Beast of the Revelation with the lion, bear and leopard beasts. All four of Daniel's beasts are alluded to in John's description of the Beast (and in reverse order, for some reason). John is not saying that the Beast is identical to the Daniel's 'dread beast'. Despite the similarities, there are also major differences.
Daniel 7 identifies the 'ten horns' as ten kings, with the primary antagonist being the eleventh 'little horn', heavily implying that they are sequential. The Beast of the Revelation instead identifies the primary antagonist as being its seven heads/kings, while its own ten horns/kings take the backseat as being inferior to the seven head/kings.
Daniel 7 has the 'dread beast' being condemned and slain and burned in the river of fire before the 'son of man' figure even appears in Daniel's vision. The son of man is not given credit for the dread beast's fate. In contrast, the Beast of the Revelation is personally defeated and cast into the lake of fire by Jesus. The courtroom scene only takes place after this has happened.
The Revelation's usage of all four beasts from Daniel 7 (and not just the 'dread beast') is not meant to identify them as the same kingdoms. John is reapplying the imagery from Daniel 7 through midrash; he is giving meaning and relevance to a new situation (Christians being oppressed by Rome) by reflecting upon an old situation (Jews being oppressed by Babylon, Media-Persia, Greece, and Syria).
The Son of Man
Yes, Jesus calls himself the 'son of man', as the Apostles do later on. On a few occasions, this is tied into the son of man 'coming on the clouds of heaven'. What is happening, however, is not that Jesus and his Apostles are saying 'Daniel was talking about Jesus'.
Within the scope of Daniel, the 'son of man' figure is solely explained to be 'the saints of the Most High'. What Daniel 7 says about itself takes precedence over what Christians traditionally assign to the vision. The four beasts are personifications of four pagan nations: Babylon, Media-Persia, Greece, and Syria. The son of man is not an individual, it is the personification of a single nation: Israel.
The image of the 'son of man' is given to Israel to exemplify the nation's role as modelling 'true humanity' to the Gentile nations. True humanity is righteous, obedient to God, and within the scope of Daniel's vision, this is what Israel fulfills through its faithful endurance during the persecution of Antiochus IV Epiphanes, and hence the application of the 'son of man' image. For the 'son of man' to 'come on the clouds of heaven' is explained in Daniel 7 itself to signify God's vindication of the persecuted saints. They overcome their wicked, beastly oppressors through their faithfulness to God.
Jesus, as the Messiah (i.e. King of Israel), is the representative embodiment of Israel. The metanarrative of the gospel of Matthew stresses this point a great deal. Jesus is Israel, as Israel was intended to be: sinless, righteous, obedient to God. Hence, Jesus reapplies Daniel's image of the 'son of man' for Israel to himself. He is true humanity. Add to this, Jesus suffered oppression and persecution from the corrupt religious leaders, culminating in pagan Rome and apostate Israel crucifying him.
At his trial, the high priest asked Jesus, 'Are you the Messiah [i.e. King of Israel]?' Jesus' response, 'It is as you say. And hereafter you will see the Son of Man seated at the right hand of Power, and coming on the clouds of heaven.' Jesus isn't prophesying a second coming here, and he isn't claiming to be the fulfillment of Daniel 7. What he is doing is reapplying the imagery from Daniel to himself. The priests knew Daniel was talking about the vindication of Israel. For Jesus to combine imagery from Daniel 7 and Psalm 110 and reapply it to himself, he was effectively telling the priests that he was their King and would be enthroned soon. But more than this, he was telling them that they had become 'the beast', while he was 'true humanity', the personification of Israel, and that he would be vindicated from their persecution of him.
In short, Jesus and the Apostles already know that Daniel 7 was about events in their past. They are not claiming that Daniel 7 was a prediction about Jesus. What they are doing is using the image of Israel being vindicated by God (the son of man coming on the clouds of heaven) in midrash for Jesus' own vindication by God.
The Abomination of Desolation
The same thing as the above items can be said for this. The 'transgression that causes desolation' (Daniel 8), the decreed 'desolations' (Daniel 9), and 'abomination that causes desolation' (Daniel 11) each refer to the same event: the desecration of the temple by Antiochus IV Epiphanes (recorded in 1 Maccabees 1.54).
Jesus interprets the 'abomination of desolation' from Daniel's visions in midrash, applying the label to a new event that would take place sometime between 66-70 AD, causing yet another desecration of the Second Temple. The differences between the Daniel's original and Jesus' midrash is apparent. The 'abomination of desolation' from Daniel's visions takes place as an act of persecution from the Syrian oppressors of Israel. The 'abomination of desolation' from Jesus' midrash takes place as an act of punishment from God upon corrupt Judea.