Religion (and other civic associations) provide an outlet for public opinion that is often critical of the nation-state.
Outlawing religion doesn't work unless there are no other civic institutions such as unions, political parties, and local governments.
Religion is always the way to speak out against the nation-state even if the leaders are chosen by the state because the prayers of groups of men can be done without leaders.
The archaeologists need to know about the rain patters in the period and place where the Maya existed because the rain was crucial about the growth and well being of the crops that this civilization used. A longer drought than usual can make a huge problem with starvation, and that can be a key reason for the fall of one of the greatest civilizations in the Americas.
''The Maya world probably had too many people'' refers to the food supplies available and their reserves, and the amount of people that were using them, so it is thought that the Maya had too many people that produced and used limited amount of food, so their reserves were very low and would have lasted for a very short term period of time.
Communism failed to provide incentives for workers and citizens to work hard and be productive. While there are many benefits from equality, if pushed to an extreme it robs people of an incentive to make an effort. There was little if any reward for hard work or innovation and a lack of punishment for poor or inefficient work. The lack of incentives was a major reason for the poor performance of Eastern Europe economies.