I was playing assassin's creed and you have these random groups of Byzantines who pop up and try to overthrow the sultan. I know how historically inaccurate this game must be, but it had me wondering about the fall of the empire. Was it that sudden ? Were there any important conspiracies or rebellions to restore the Byzantine empire ? Thanks !
In addition to what has been said earlier, Constantinople was heavily depopulated by the time of the conquest and reduced to a series of villages within the walls. Hence, the years after the conquest were devoted more or less to the repopulation of the city either by encouraging the return of Byzantine exiles or or by resettling other Greeks, Jews, and Turks in the city. As for your question about conspiracies; there was no real hope of restoring the Empire but certainly there were some number of Greek nobles who may have plotted against the Ottoman Empire. However, the the Ottomans were very skillful both in encouraging cooperation with promises of exemption from taxation(or at least no additional taxation) for the population as a whole and enshrining the authority of the non-Muslim clergy to secure their independence from the Latins(hence the phrase "Better the sultan's turban than the cardinal's hat"). For a very interesting primary source on Istanbul in the aftermath of the conquest(an extensive record of the city's demography), see:
Inalcik, Halil: The Survey of Istanbul 1455: The Text, English Translation, Analysis of the Text, Documents(Istanbul:Türkiye İş Bankası Kültür Yayınları, 2012).
The Byzantine Empire, as previously mentioned, had long been in decline and by the time Constantinople fell in 1453, it was reduced to a small area surrounding the city itself and the Greek Peleponnese peninsula. Capturing the city was the Ottomans' way of bringing the empire down for good.
The Peleponnese section fell into chaos with different factions fighting over who would be in control. The Ottoman Empire took over that area too, eventually (IIRC).
The Pope in Rome was outraged by the loss of a Christian ally in the east and demanded a "crusade" of sorts be mounted to reestablish the empire, but other nations were uninterested and nothing came of it. I'm not sure of any further plans to restore it.
There were actually two families that retained claim to the Empire following the Fall of Constantinople in AD 1453 and the Fall of Mystras and Trebizond in AD 1461.
The Palaiologos family, who ruled as the official Byzantine Emperors in Constantinople (and a separate branch in the Morea) until the fall, retained their claim for at least 50 years before the family faded into obscurity. Andreas Palaiologos, who claimed the title of "Emperor in exile" was the last legitimate heir to the Byzantine throne, but he sold his title to the King of France in 1498 and passed away four years later in 1502. However, despite this, any of the descendants of the Palaiologoi could have theoretically claimed the title of Byzantine Emperor after this point, but none really seemed interested in doing so.
The other family, the Megas Komnenoi of Trebizond faded into obscurity shortly following the capture of their capital in AD 1461 by Mehmed II. The family fled to Georgia and lived out the rest of their days in foreign lands.
Of these two families, only the Palaiologoi really made any serious attempt to take back the Empire. They tried to rally the Pope and the power of the Italian states, where they resided, to take back the Queen of Cities, but to no avail. Western Christendom was threatened by the rapid expansion of the Ottomans - to launch a full on assault on their capital would have been suicide. Additionally, the City of Constantinople was in shambles when it was lost: the Theodosian Walls were crumbling, there were large empty and ruined patches where people once lived, even the Hagia Sophia was starting to show signs of wear. There was little to gain but glory in taking it back.
Later on, once the city had been repaired by the Ottomans, there was little ability for Byzantine Greeks to challenge the authority of the Sultan, who held an enormous amount of wealth and power and who swayed many to his side. There just wasn't enough of an incentive for the remaining Greeks to rise up in rebellion against their new overlords. It was either support a somewhat similar lifestyle in your homeland under the shadow of the relatively civil Ottoman "conquerors", or flee far away to the lands of the "treacherous and vile" Latins, who were the ones who stabbed your Empire in the back in 1204, and who abandoned your people in their hour of need in 1453. Which would you choose?
No the fall of the Byzantine empire was not a sudden event, it had been happening for centuries, with the 4th Crusade rapidly accelerating the empire's fall. As for the other questions i do not know