I'll give some of these questions a shot including u/sloes, and hopefully answer what I can and maybe someone else can give more details. Constantinople had already been depopulated prior to the 1453 siege and had never fully recovered from the 1204 sack by the crusaders. Right before the final Ottoman siege, roughly only 5000 Greeks and 2000 foreigners, largely from the Italian peninsula, were able to man the walls of the city against the Ottomans. After the fall of the outer walls, many defenders, supposedly including emperor Constantine XI himself, took to fighting in the streets and died in combat. I apologize for the lack of scholarly sources because I don't have my books at the moment, but according to John Julius Norwich's A Short History of Byzantium, the Turkish sailors who were meant to blockade the city had gone inside the after its fall to begin the plunder and rape. This allowed several Byzantine and Venetian galleys to escape the naval blockade after walls were breached, but the population of Constantinople had already been leaving the city in the years prior. Norwich tells us that yes, many of the women and children were raped or impaled by the plundering army and others indeed fled the city or were enslaved.

I'm not sure of any instances of forced conversion in the aftermath of the siege, though Mehmet II did invite many of the former Greek residents back into the city to repopulate Constantinople as the new Ottoman capital. Obviously, Turkification was extremely gradual and even by 1923, it took a mass population exchange to wipe out thousands of years of Hellenic presence on Asia Minor.

The process of Turkification in Anatolia began right after the 1071 Battle of Manzikert, when the Byzantines lost almost the entirety of Anatolia against the Seljuks, continuing with the establishment of the Turkish Sultanate of Rum, largely based in central Anatolia around Iconium. Byzantium did recover the coastal regions in the Crusades thanks to the Komnenian restoration, but it was never again able to control the interior of Anatolia, let alone all of Anatolia - this was ensured by the Byzantines' defeat to the Seljuks at the Battle of Myriokephalon in 1176 AD, after which they never attempted to reconquer it. Byzantine Emperor Manuel II Palaiologos (1391-1425) was forced by Ottoman Sultan Bayezid I to provide military aid and accompany him in Bayezid's wars to consolidate and unify Anatolia under Ottoman rule. Manuel was able to visit former Byzantine lands in Anatolia and while there, look at the remnants of Greek/Roman political rule. For example in Ancyra/Ankara, he noted that descendants of the Byzantines there were often able to speak both Greek and Turkish, and could translate for those that spoke no Greek. Clearly, Turkification was underway in the Greek-speaking peoples of Asia Minor, where Byzantium had not had political control for decades, if not centuries. Eventually, we can assume that with continuing Turkish rule under the Ottoman state, and the benefits associated with converting to Islam and adopting Turkish customs, speaking Greek had less and less of a purpose for these descendants of the Rhomaioi.

I'm not really familiar with the rest of Ottoman history and the genetic makeup of modern Turks, so I hope someone else can answer that, as well as the numbers on the ethnic/religious makeup of Anatolia.

But yes, since Mycenaean times, Greek civilization has had a long history of settlement on Asia Minor, especially on the coasts. As for central Anatolia, it was dominated by indigenous Anatolians speaking languages that formed the Anatolian branch of the Indo-European languages, now extinct. This was due to assimilation and the continuing and gradual Hellenization of central Anatolia beginning with Alexander's conquests, and by the 1st century BC, the Anatolian languages had largely been replaced by Greek. Central Anatolia was eventually largely Hellenized and this was brought about by continuing Hellenistic political control of Asia Minor, despite central Anatolia's more remote and mountainous nature, continuing with Roman and Byzantine rule. During the Slavic migrations into the Balkans in the 7th and 8th centuries, Anatolia remained the stronghold for Hellenic civilization due to Greece itself being raided and populated by migrating Slavic peoples. In fact, because of this, the emperor Nikephoros I had to resettle Greece itself with Greek-speaking families from Anatolia.

Sources: A Short History of Byzantium - John Julius Norwich

"Manuel II Palaeologos and His Müderris" - Stephen Reinert