The Ottomans -- as well as Genoa and Venice -- faced severe economic shortfalls when Portugal began running amok in the Indian Ocean. By the mid 16th century, with Portugal now boasting a sizable permanent presence in the Indian Ocean (Goa was acquired in 1510 and would remain Portuguese until the 20th century), Portugal's dominance of the spice trade would prove problematic for the Mamluks (briefly; the Ottomans conquered Egypt less than a decade after the Portuguese acquired Goa) and later the Ottomans. This then had a knock-on effect of reducing the economic viability of Venice and Genoa. Venice in particular was rather dependent on the spice trade and losing that trade permanently was a rather serious problem. To compensate, Venice began pursuing territorial expansion rather than trying to dominate the Levantine trade. This put them in direct conflict with the Ottomans and the Venetians often fared poorly in those wars.

As for the Byzantines allegedly hating the west, that's very much true. The Fourth Crusade was a remarkably shameful display by the crusaders and it set the stage for future clashes between the Byzantines and the West. Ertugul Ghazi (father of Osman, for whom the tribe is named), and the various beyliks like him, would likely have found the Byzantine Empire a much tougher nut to crack if the Byzantines hadn't just about been destroyed in 1204. It's worth noting that Ertugul's conquests were made at the expense of Nicea, the Byzantine successor state that would eventually reassert Greek rule in Greece. It's hard to believe they wouldn't have been better prepared if they were not also occupied with thwarting the "Latins" in Constantinople.

But were the Byzantines without friends? No. Genoa cooperated with Constantine XI extensively during the last great siege; it took the threat of an Ottoman invasion of their town (Galata) to force them to stand down. And the Byzantines also benefited from assistance from several other nationalities. Italian captains risked running the Ottoman blockade to beg for relief on Constantine's behalf; Constantine also appears to have been willing to recognize the Pope as primus inter pares if the Pope would lend assistance. The Byzantines even begged the Venetians, whom they still despised, for aid; the Venetian Senate hemmed and hawed until news reached them that the city had fallen, at which point they all appear to have burst into tears or something.

Neither side was particularly "good," honestly. The Ottomans showed a remarkable degree of religious tolerance (although substituting a jizya for the devsirme is... morally questionable) and the millet system (essentially independent religious courts for different religious groups) was a rather good solution to the problem of differing religious laws in a pre-secularization era. But it's worth noting that the Ottomans were merely one of dozens of different beyliks that wanted Byzantine blood. If Ertugul's successors had failed, it simply would've been a different group -- the Karamanids, perhaps -- who would've likely finished the flagging Byzantine empire off.