Just a few questions before i finish the update:
When the Greeks in Anatolia converted and assimilating to Islam and Turkish resepectively in the middle ages, how did it work and how long did it take for the Greeks in Western Anatolia to convert and assimilate till there was a Turkish majority?
Western Anatolia is still at least a good part Greek and Orthodox for over another century from your POD, but I don't know how quickly things changed from there.
How long would it take for the Turks in Central Anatolia to become a minority and to convert to and assimilate to Orthodox and Greek respectively?
Several generations to make it deep rooted, but you can probably get Greek speaking fairly quickly after conquest. Orthodoxy probably takes longer.
Assuming minimal (borderline?) ethnic cleansing - y'know, the Byzantine practice of breaking up groups they found to be a problem and moving them across the empire, so that you'd see Serbs put in Anatolia and Turks put in (what is now) Albania. . . I'd guesstimate in the range of the late 13th century, but that's pulled from my hat.
The Crete was retaken in the 10th century and as far as I know is pretty clearly successfully remade before the end of the Macedonians (mid-11th century) - but that was a smaller area.
Still, it's one of our best examples of the Byzantines reByzantinizing a place.
The old Bulgarian Empire's lands were at least semi-Hellenized by this point (the 1170s), but religion wasn't a factor.
Is there any value of using spearmen in tightly packed spaces against other infantry (mostly light infantry with bits of heavy thrown in)?
Yes. Spears are boringly standard infantry weapons, at least in the West, but versus nonspearmen - spears have reach. Very useful.
Of course, if those foes get close enough that the spear reach advantage is not an advantage, that's a problem, but the spearmen should have a secondary weapon for those situations - a short sword, probably.
Would Varangian Guards tear apart other infantry and cavalry? How long would it take?
Let me put it this way: Yes.
They were extremely effective at what they did - although I wouldn't want them vs. cavalry except on their terms.
Also is there a website where i can type in the name of a city in and then it comes up with a Greek name, which is written in English, i think it's something to do with etymologies (Istanbul - Konstantinoupolis, Syracouse - Syracouses, Trebizond - Trapezous, Antankya - Antiocheia etc)?
There might be, but I don't know of it.