"For the good of the people" means "in the best interests of the citizens". It's an important distinction that the line does not mean that the government should always make the most popular decision. It's saying that the government should always consider what will most benefit the people that they represent or rule.
The second line (follow in everything the general will) does suggest that the government should make the popular choice.
As a whole and without further context, the author is suggesting (wrongly, in my opinion) that the best interests of the people are served by always making the most popular choice.
"Will" in this context means that which the people want and desire. So the government should do what the people want.
It is every parent's "will" that their child be healthy. As children, it is our "will" that our parents always treat us fairly.
EDIT: I addressed the quotes you listed, please do not assume that the answers address the essay in its entirety.