What's the point?

As I have been reading The Republic, there are a few things that I have to keep reminding myself of...
1. In Books 2 & 3 Socrates is no longer arguing a point, but rather he is trying to "persuade Glaucon (and friends) truly" (Pg. 35)
2. Socrates' goal is to reach truth, and to encourage others to seek this truth
3. Socrates and friends are creating this city "in speech" as a broader way to examine the just and unjust in a person ("If we should watch a city come into being in speech... would we also see its justice come into being and its injustice?") (pg. 45)

And then they create a city based on their (aka. Socrates') idea of what a city should be. He sets the criteria that each person should devote themselves only to one thing (reversing this verdict later), determines what the poets can write, how the gods should be portrayed, states that "no one will possess any private property except for what's entirely nessecary" In Socrates' description of the city, he effectively creates one in which every little detail is designed with the best intention for the state.

But the question that I keep coming up with is, To what extent do the critera set for this city reflect the true opinions of Socrates? Or, are they just ideas from the point of view of a leader who wants the best for his state? Also, if the point of this allegory is to find the origin of justice and injustice in the city (as I earlier stated), then do the details of the city, as to it's particular view of the gods, etc. really matter in the long run - after all, isn't Socrates trying to learn the true nature of justice and injustice so that he may apply them universally - across cultures? Or maybe this rises a new question. To what extent can justice be applied universally? If the truth is rooted in the nature of how the city runs, then does the same truth apply in a different city that runs in a different way? Is the truth of Justice different for every person? Can one true justice exist among humans?

I commented on Olivias