I'll leave it to someone better qualified to answer the first part of your question, but I can answer the part about the books in Constantinople in its last decades under Byzantine rule and following its fall in 1453.

We know that in 1423, the Greek classics were used by the Byzantines as a piece of diplomatic leverage, playing to Italy's fascination with classical culture. Emperor Manuel II sent his Latin secretary, Giovanni Aurispa, to Italy with 238 Greek manuscripts from the imperial library.

Thirty years later, Constantinople had finally been conquered by the Ottoman Turks and we are lucky enough to be given details of what happened to the books in the city in the aftermath. The historian Doukas arrived in Constantinople mere weeks after the sack of the city and reports the following:

Innumerable books were loaded onto wagons and hauled in all directions; they were dispersed throughout the East and West. For a single gold coin, ten books were sold - the works of Aristotle and Plato, books of theological content and on every subject.

Another contemporary, Michael Kritovoulos, also reports the fate of the books:

And holy and divine books, and others mainly of profane literature and philosophy, were either given to the flames or dishonourably trampled under foot. Many of them were sold for two or three pieces of money, and sometimes for pennies only, not for gain so much as in contempt.

Both sources make the point that both theological and secular books were harmed in the sack, as well as saying that books were sold on at much lower prices than they were actually worth.

There were of course exceptions to this, and people who escaped before and after the fall undoubtedly took some literature with them, many of which adding vital fuel to the accelerating Western interest in classical culture and ideas.

Sources: H. J. Magoulias' translation of Doukas' Decline and Fall of Byzantium to the Ottoman Turks, 240 and C. T. Rigg's translation of Kritovoulos' History of Mehmed the Conqueror, 74.