Did the idea of a unified Egypt precede the actual fact? I mean did they see those lands as naturally belonging together under one pharaoh? Something like 19th century Italy where unification was widely supported by people from all classes. Or was this a conquest that just stuck for a long time?
Images of pharaohs wearing a double crown suggests that they believed those crowns could be combined, rather than inventing a third one to represent rulership over the new Egypt.
I understand sources from this period are rare if non existent. Is there anything known except basics?
I'm not a historian of Ancient Egypt, but antiquity is something I've studied and that I am very much interested in, Egyptian history comes up a lot in antiquity. I'll try to answer as best I can, but I'm sure an Egyptologist could provide more information to answer your question.
It's true that we have few sources from this era, although we have some beautifully preserved works of art featuring Narmer, the king who united the two kingdoms. We also have earlier historians to turn to, the infamous Greeks who started the pursuit of history. Keep in mind that the unification happened some 5000 years ago, so if we want to get an idea of how the unification was viewed, we have to resort to reasoning, and reading between the lines of some questionable sources.
Seen here is the Palette of Narmer, on one side we see we see Narmer, wearing the crown of lower Egypt (the Northern Half), engaging in conquest as he is about to strike down a man, and on the other, Narmer is wearing the crown of upper Egypt (southern half) (my arts history professor insists he's wearing both crowns in this scene) with an army at his side, and his enemies beheaded. All around is religious imagery, most notable are the two lions with intertwined necks, interpreted by arts historians as a symbol of unification. Narmer is featured in hierarchic scale, he appears larger than the other figures, suggesting some sort of divinity to Narmer.
Today, Narmer is commonly identified as Menes, a pharaoh from around the time of unification, though we don't have many works on Narmer, we can turn to the Greek historians for some information on Menes. Diodorus Siculus, a Greek historian writing Historical Library (as his book was known to later historians) mentions Menes as being a very pious king who popularized the religious practices of Egypt that became a custom of the land. Strabo, writing in Geography, says that the priests of Egypt claim Menes to be the "first mortal king of Egypt", that below the ancient Lake Moersis (a lake that was close to the divid between upper and lower Egypt) there was nothing, that the land of Egypt was empty during his time. Strabo probably got that idea from Herodotus, the father of history, who also asserts that Menes was this first Egyptian king. Roman historian Pilny the Elder in his Natural History mentions Menes as having invented writing for the Egyptians. We certainly get a pretty benevolent picture of this conqueror.
Less time has passed between now and the time of the Greek historians than between the Greek historians and the unification of Egypt, even then they were writing about events that happened thousands of years ago. Naturally, the writings of Greek historians should be taken with a grain of salt, but by looking at the Narmer's art, we can draw a line between him and Menes, we can also see that Narmer was no stranger to piety, as we see with his heavy religious symbolism. The difference in names comes from our poor understanding of how the Egyptian language evolved (for instance, we don't have the slightest clue what spoken Egyptian was like), and the name Narmer is taken from the inscriptions of the tablets. If he captured the hearts and minds of the people he conquered, he probably would have done so through religion. Combining both crowns could be seen as a symbol of respect to the people he conquered.
To conclude, we can't say for certain how the Ancient Egyptians viewed the unification, if they saw it as conquest, or as divine justice. We also don't what sorts of policies Narmer/Menes implemented on the conquered upper Egypt, if they were under tyranny or famine, or under some benevolent rule, it's uncertain. But as the priests (supposedly) told Herodotus, Menes/Narmer was seen as a great king to be respected, a father of a nation. The unification was certainly conquest, Narmer/Menes did not hide that fact as seen by the beheaded corpses on the Palette of Narmer, but to the Egyptians of later generations, it must have been told as a great myth, some divine justice that brought them together, rather than bloodshed and suffering, even if it were not so.
