The harmony is hierarchical, not egalitarian. When the hierarchy is inverted, we have injustice. Justice is individual before it is social. Robinson Crusoe alone on his desert island before Friday shows up can still be just or unjust. We are just or unjust to ourselves before we are just or unjust to others.
Justice is rightness, righteousness.
No, it is not. We can talk about it and derive an ethic from it. For instance, we can discover that it has three distinct faculties or abilities or powers. From Plato to Freud, common sense, philosophy, and psychology have found themselves talking about some version of this tripartite-soul idea, with virtue as its health. This is natural, like a heavy body falling to its natural place, or a wanderer returning home.