A lot of this is coming from Hunt's The Medieval Super Companies, but the entire bibliography would be a bit longer if I was pressed to provide more citations. I would like to begin by saying that medieval economic history has changed significantly since Renouard's history of Florence. Furthermore, if you're interested in the subject, Najemy's history is currently the standard history of Florence in English, and probably represents the standard for Florentine historiography across the standard scholarly languages, but I'm not as familiar with Florentine historiography as I am with Venetian and Genoese historiographies.

• Personally, I would argue that no single city represents the "main economic center of Europe" in the later central Middle Ages. Northern Italy and the Low Countries were certainly the most urbanized regions of Europe and were the two major commercial centers. By the 14th century Florence was certainly one of the largest cities in Italy and certainly a center of manufacturing, particularly textile production, but both Genoa and Venice both had colonial empires that fed the commercial trajectory of the two cities. It's hard to say which of these cities had the largest economy, but definitive claims of Florentine primacy are suspect. Also, Catalonia was beginning to become a significant commercial power as the crown of Aragon pushed into the Mediterranean.

• One of the traditional arguments for the economic crises of mid thirteenth century Florence was the fact that the kings who borrowed money from the great banking families of the Bardi, Peruzzi, and the Acciaioli defaulted on their own. Hunt's work, however, demonstrates that these loans, while hastening the decline of these companies, was not the definitive cause. Rather, poor harvests and other agricultural crises in the Mediterranean was the major catalyst for decline as these companies made most of their money as essentially holding companies for bulk goods such as grain. Not 100 percent certain about security, but I have to guess that they had no security. They were not forced to grant the loans.

• Not sure what you're getting at or what you mean by "fall," but the gradual increase in Medici influence over Florentine affairs happened in the early to mid fifteenth century under Cosimo de' Medici. Yes, Medicis appear in the public record at the end of the fourteenth century, but the events that allowed the Medicis to rise through the social ranks of Social society are mostly internal and probably have their origins in the social pressures that caused and were set in motion by the Ciompi revolt.

That being said, Medici control over the Florentine political process, while significant, was nowhere near as absolute as older scholarship suggests.

• Francesco Pegolotti was a factor for the Bardi company (one of the three largest companies in early 14th century. He wrote a commercial manual that describes, among other things, commercial centers and what could be purchased there. The city that is furthest east that he described is Trebizond. He also describes commercial agreements in place in these urban centers. He mentions that the Bardi had established agreements on the Turkish mainland, but there are very few for Florence generally and I doubt many Florentines actually went to Trebizond. Judging the evidence of Pegolotti, the Venetians and Genoese dominated commerce in the eastern Mediterranean.

• This is kind of an impossible question. The Song dynasty (13th century) did help to facilitate a massive commercial revolution that further developed a massive and wealthy economy. Although the Yuen Mongol dynasty mismanaged that economy, the Chinese economy was probably larger and wealthier than that of Europe. Kind of impossible to answer though.

Before European Hegemony is a fine book on global trade. Certainly outdated in a number of ways, but still a useful text. I believe Steven Epstein has a introduction to the high and late medieval economy.