Well the genetic makeup of Turks living in Turkey is different than the genetic makeup of Turks living in Central Asia (as can be seen if you look at our faces).
Turkish genealogy is a melting pot, which is pretty understandable given the size and the location. There's no such thing as a "pure" Turk gene.
They had lower population because they were migrating, the lands they came from could not support high populations, they had inferior culture, they had inferior technology, they couldn't have adapted to being settled easily.
Exactly the same could be said of the Mongols. And look how far they got. Nomadic =/= primitive, the Mongols themselves were fielding troop numbers which would not be seen again in Europe until Napoleon. It's not actually surprising, the steppe nomads militarised their entire population, every man could ride and fight from horseback. Whatever settled people existed in Anatolia on the other hand likely had a small military class, the rest would be farmers and goat herders. I don't know about you, but I'm thinking an army comprised of people who's most dangerous foe to date was a particularly stubborn wolf isn't going to win when pitted against people who consider filling you full of arrows from horseback a national sport.
Than how come they changed the demographics of Turkey this much?
They didn't, they changed the culture. As to how, look at Britain and the Normans, exactly the same thing happened there. It's not that difficult, replace the nobility with your own culture and suddenly everyone starts copying you. Partially because everyone would like to think of themselves as members of the nobility, and partially because doing what the nice men with swords say tends to be a good survival strategy.
How the hell were a bunch of nomads that never saw a sea before capturing Constantinople using ships a hundred years after they founded their first city in Anatolia?
Because real life doesn't work like Civ where everyone needs to research tech separately. If you live somewhere surrounded by ship builders and ship sailors it doesn't exactly take a huge amount of effort to get them to explain this boat concept to you. Furthermore, as you note the Turks didn't come in, wipe out everyone and then breed like rabbits to take over the land, they came in and subjugated the existing population, who were quite likely to already know about boats. And more than likely the guys actually sailing them, what with them effectively filling the role of the working class.