Or would we see a reconquista sort of event later on with orthodox Christians taking back land that used to be their’s like what happened in the Iberian Peninsula with the Catholics?
This probably. For all that many orthodox have consistently opposed Rhomanoi supremacy, they aren't totally stupid about it. Having the center of the Orthodox world fall to Muslims would be too much of a threat. Not only is Anatolia too crucial as a stronghold to hold the line between Orthodox Christianity and Islam, but if they didn't then the Catholic nations would. Before Basil III killed the Kingdom of Jerusalem and other Crusader states, Catholicism was really into crusading. Afterwards, they never quite forgave Byzantium. Constantinople falling would be interpreted as a sign of weakness that Catholics would use to overrun the Orthodox world.
Speaking of the wealth of Constantinople, how would a Muslim Bosporus operate? Would Russia, have to rely on the Baltic Sea? What about Georgia, Armenia, and Bulgaria? What happens to their navies? What about trade? Does less trade with Eastern Europe lead to an earlier trip by Columbus to the New World? If so, which country finances him? Does he land in America? Or does he land in Columbia?
OOC: America=North America, Columbia=South America
Badly. Trade in the Black Sea was dominated by Orthodoxy and the Mediterranean by Catholics. Muslim interference in the delicate balance of economic diplomacy between the two would piss everyone off. The turks showed no sign of naval skills that would indicate they would be able to control the naval situation. Constantinople needs a strong navy to flourish. Under the Turks, it would have withered. No doubt.
Why would Russia have focused on the Baltic? Ever since the Mongols, Moscovy has been orientated south. During the Mongol yoke, Novgorod the Great gained too many privileges from excessive tribute and flattery to be influenced by Moscow unlike many. After the Mongols, keeping Novgorod as a buffer zone was a major part of their foreign policy. It ensured the safety of their northern front. Unless the Livonian Order and later the Norse tried to attack Novgorod, something Novgorod did a good job of preventing by only requiring a single port on the Baltic and not keeping a war fleet, Russia would prefer its OTL goal of driving south to the Black Sea.
The Black Sea still would have become a major naval battlefield. How could it not be? Anyone gaining true dominance is stretching belief. Anytime the Rhomanoi and later Russia got close, everyone else would ally.
The Age of Discovery probably remains the same. Egypt was the problem there, when it started focusing on trade between India and the Mediterranean. Venice's economic privileges there produced its Golden Age of Expansion, which led to Spain focusing on developing oceanic trade to reduce the Mediterranean dominance. America would always have come about from the Norse and Hansa seeking to outdo the others in their expanding trade networks, and then it wouldn't take much for other Atlantic powers to follow a similar course of expanding their trade networks to new lands. Venice's growing dominance in the Mediterranean trade was simply the catalyst. While America was better known, it was firmly in the Norse and German spheres of influence. Spain had no interest in fighting them, not like they were Venice. Columbus was sent to round Africa for India. He only discovered Columbia by accident when he went too far west after a storm.
Edit: Woops. Clash with previous post. Maybe the Hanseatic League extended to Limerick, or maybe a competing Norse trading network. Then it just happens North and South America were discovered by two Columbus'.