What type of government existed during the middle ages?

Feudalism is the right answer.

Explanation: In medieval era, before the birth of modern nation-state system, feudalism was the only form of government used to rule people. People belonging from upper nobility such as Kings or High ranked military officers were allowed to rule over people. He was the lord of people and their land.

b: the establishment clause  

b: socialism  

the conditions that made the byzantine empire vulnerable to attacks by the muslin turks were the sack of constantinople by western crusaders, the conquests of the sultanate of rum, presence of rival kingdoms and finally the set up of fiefdoms at the empire which were owned by the ghazis (turkish warriors).