Was their appearance significantly different and if so, would that have even mattered when considering how Greek they were? Were there any other factors which would differenciate them from people from 'Greece proper (you know what i mean)'?
Insofar as there were cultural divides in Byzantine society during the middle period - and there were a lot of them - they weren't generally between Anatolian inhabitants of the Empire and the ones in Europe. The urban/rural divide was much more interesting, but it was only in Anatolia that this mattered for a long time, if only because the Empire's only territory in Europe
was a couple of coastal cities (until Eirene and Nikephoros I fought their Slavic wars). Athenian notables like Eirene Sarantapechaina's family weren't really different in any regionalizing ways from notables in, say, Ephesos.
Now, during the eleventh century, it's been argued that there was a genesis of identity among the magnates of the Anatolian plateau - basically analogous to the rich herders of the American West, right down to the fact that they had to fight off jihadi cattle rustlers - and that this is visible in literary traditions like the
Digenes Akrites, an epic poem, and things like the testament of Kekaumenos Katakalon, who wrote a guidebook for his son. I think this is all well and good, but that one mustn't overstate the political or social importance of these Anatolian aristocrats - highlighting their regional frontiersman stockherding culture is one thing, but claiming that these men were mounting a threat to state central authority in the manner of French nobles at the same time is entirely something else, unsupported by the evidence. And, of course, this is
aristocratic culture, not shared by anything but a certain slice of society even in the region to which it applied.
Anatolia was mostly Greek before the Turks got through. It became rapidly Turkish because the Byzantine landowners had turned Anatolia into a huge pasture to grow their sheep. The primarily pastoral semi-nomadic Turks could quickly move into these lands as a result. Then, as the Byzantines figured that Anatolia was a lost cause, they made population transfers as part of peace treaties, futher "Turkifying" Anatolia. I don't think that the loss of anatolia was a huge blow to Byzantine manpower, as is often said, but a major blow to byzantine income, which had come before from two major sources, anatolian pastures and Constantinopolitan trade taxes and sound tolls. The crusader disintegration of the Byzantine heartland had a much larger impact on manpower.
I agree with almost everything here - although I can't quite imagine what other kind of economy the Anatolian Plateau could have had, if not a pastoral one, and the way I read your post you're implying that it could've been good for something else.

But I don't think (well, this isn't my opinion, it's Jean-Claude Cheynet's

) that the loss of the Anatolian plateau was particularly bad for Byzantine state finance in a direct sense. Financially, the early Komnenoi were in much the same situation as were the later Makedonian emperors. The western Anatolian coastline and even, arguably, the ephemerally-controlled Byzantine Syrian territories were much more important than the plateau in terms of manufactures and agriculture.
What the loss of the plateau did was create a strategic context that made it almost impossible for the Byzantine state to hold onto what it had. Instead of being able to concentrate defenses at the Taurus Mountain passes, which had been the course of action since the Herakleian dynasty, the Komnenoi were forced to heavily garrison points all around the Anatolian coast,
all of which were vulnerable to attack from the plateau. The first three Komnenoi pursued offensive operations to lessen the defensive burden on these places, but that took military competence that not all emperors were bound to share, and ultimately, with Andronikos I and the Angeloi, it turned out that they didn't.