1. One similarity between the social structures was classes. Almost all ancient civilizations naturally developed similar social structures, as this one social structure was the best, at that time, for building a strong nation. They had a head of government, who was basically a king, and at the bottom you had peasants or slaves. The middle would have merchants and warriors, and above that would be politicians and statesmen. Although they went by different names in these different societies, the concepts were more or less the same.
2. Obviously, if the top of the social hierarchy, (the king or its equivalent,) were to fall, the political landscape would change quite abruptly. You would now have someone new in charge, who would most certainly be different than his predecessor, (assuming the overthrow was because a group of people with different ideologies assumed power for themselves.) Although not always the case, it could affect the day to day lives of the citizens. For instance, if he has a different stance on taxes on foreign goods, (whether to raise or to lower them,) the common merchant would have to deal with this new law.
3. One way in which monarchs and different leaders were able to withstand challenges was because they were absolute monarchies. They had total and complete power over their domain letting them basically do whatever they wanted, and making it much harder for anyone to find allies in a revolt. (Because everything was controlled by the person you were trying to overthrow can get rid of you and your allies at any time as he has power over your job and the army, either of which can oust you.)