What went wrong and what can aspiring societies of today learn from past mistakes to forge a stable civilization outside of the white homeland?
It wasn't a single, identifiable thing that went wrong. It all happened because the Rome fell.
If the Western Roman Empire didn't fall, There wouldn't have been crusades to call on by what was left of the Roman Catholic church -- because there wouldn't be feudalism and all the internal instabilities that come with it.
And if there aren't any crusades, the sacking of Constantinople would've never happened.
Actually, the traditional name was "Kostantiniyye," a Turkification of "Constantinopoulis." "Istanbul" is believed to derive from a a saying meaning "the place," and was a common informal name for the cultural and political center of the empire. The city was still known as Constantinople until the post-Ottoman Turks insisted that the west start calling it "Istanbul" after they adopted the Latin script.
Looking east instead of west for military assistance. No Muslim nation could be trusted past a single generation.
The later Komenians turning their back on the alliance with the Holy Roman Empire, flying in the face of everything established by Alexius in terms of geopolitics, was the first real nail in the coffin of Byzantine expansion.