Hello, I've been lurking for awhile but your question has brought me out of the shadows as I'm somewhat a student of history. I'll try and answer your questions as succinctly as possible since the issue are very long and complicated.
1. Ever wondered why Copernicus, a catholic priest, was never condemned but Galileo was for holding the exact same theories? It's because Galileo's academic enemies trapped him into moving into theology at a time when Protestants and Catholics were fighting the bitter 30 years war in Germany. The council of Trent expressly stated that only trained theologians could publicly expound on holy scripture. The Galileo myth is promoted by many secular media outlets, mainly atheists and other enemies of the church. Most scholarly history books will give you the true picture of what happened. The following website is good to get you started on the issue.
newoxfordreview.org/jun00/thomaslessl.html
2.The sacking of Constantinople was the unfortunate result of a dynastic dispute for the Byzantine throne, not for any religious reason. The Pope told the crusaders to go straight to Egypt but when the crusaders couldn't pay for the boats, the doge of Venice told them if they helped capture Zara from the Hungarians on the dalmatian coast then it would help pay their debt. This they did and were promptly excommunicated for it by the Pope. They convinced him to recind the verdict when the promised again to go straight to Egypt, but while in zara they came across an heir to the byzantine throne named Alexius. Alexius promised them all the riches they could imagine if only the crusaders would help him get the Byzantine throne. This they did, but when it came time for Alexius to pay, he blew the crusaders off. There wasn't enough money to pay them. To break an oath was a great insult and drove the crusaders berzerk. They then laid siege and sacked the city. Here's a great original source quote between the doge of Venice and Alexius before the siege:
"Alexis, what do you think you are going to do? Remember we have raised you from a very humble estate. We have made you lord and you not keep your agreement with us and crowned you emperor. Wiill you not keep you agreement with us and will you not do more?" " No," replied the emperor, " I will not do anything more." " No?" said the doge, " wretched boy, we have raised you from the mire,' and we will throw you into the mire again and be sure that I will do you all the injury that I can, from this time on."
3. The Crusades were called when the Byzantine emperor and Eastern Christians asked the Pope for help to fight the Turks. For 500 years the muslims have been conquering Christian lands. Spain had fallen, the Saracens had been moving up the Italian peninsula and the Turks had just had a major victory over the Byzantines at the battle of Manzikert. The Crusades were in every way a defensive war, an attempt to roll back muslim conquests and re-unite the two great churches.
4.Martin Luther was just one of many heretics throughout Church history. Are both Catholic and Orthodox corrupt since the heretic Arius said so at the council of Nicea? Or Nestorius? Or Marcion? Martin Luther himself at the time was no one special, just another monk from a backwater German university. But the Popes were in the hands of prominent Italian families such as the Medici's and Borgia's, all who hoped to use the papacy to unify Italy under their own families. They could care less what was going on in Germany. The problem wasn't that they taugh falsely but that they didn't teach at all and many local dioceses were falling into the hand of less than pious men. Luther himself didn't call the pope corrupt until he was excommunicated. His ideas were embraced by some german princes who wanted to usurp authority from the Catholic emperor and it was they who pressed the issue. Also of interest was that the protestants tried to get support for their position from the greek patriarch who promptly shot them down as heretics.
5. Yes some did get to be popes through connections just like some patriarchs got there through their connections, especially under the Ottoman Empire. These are very powerful offices which some people saw as a tool to advance the political aspirations of their families or principalities. It was under these men that the focus would shift from religious or pastoral duties to more political ones and when corruption would start to creep in. Again realized that they wouldn't teach religious corruption but would be too focused on secular politics to address problems that would pop up at the local level. But once things start to get out of hand, a council would be called to address the issues. This happens all the time, it's just that some people are too impatient to wait for it.
6. Rome has been at the forefront of much of the advances in Western Culture. Copernicus was a catholic priest, Popes funded classical learning and the founding of modern universities throughout Europe and much of the advances in mathematics were done by Catholic bishops in the middle ages, especially when Arabic learning was brought back to Europe after the crusades. Gregor Mendel, the 19th-century Catholic monk is regarded as the founder of modern genetics.
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