I recommend you order a book called "On Wealth and Poverty" by St. John Chrysostom. During the days close to his sermons, there were earthquakes and he speaks about God and disasters.
If you want I can type things out for you from his sermons, but it would be a lot of work and i am not sure about copyright for holy fathers... LOL
about other questions such as military defeats, as another pointed out an emperor turned towards Iconoclasm because he thought God was angry at the empire for allowing icons, since there were so many military defeats against the heathens who did not use icons. at least that is what some historians think
with the fall of the entire empire, sometimes it is blamed on the union of florence and the traitorous people who accepted it in order for a hope of secular protection, sometimes on the joint prayers in hagia sophia with the latins
I have also read though that the fall of the empire was already fortold in the city, such as a statue of Constantine pointed east, which tradition said the conqueror of Constantinople would come from the east and the moon would turn red. It just so happens there was a lunar eclipse during one of the days of the seige of Constantinople by the Turks
Generally I think in those times these occurances did seen to be happening by the will of God, including natural disasters. I believe as well that there disasters happened for a reason, although I will not try to choose one to believe. I simply believe it was God's will for these things to happen.
Today, generally more secular scholars and seminary professors do not really care for such explanations, but instead prefer a more scientific approach to these matters of history, to not say God was punishing this or that or showing this or that, but intead this event occured because of x y z historical circumstances. It just depends on who you ask