Tahir, first, I assume that what you said is supposed to work for every kind of society (whether it's Islamic or not), since Qoran is apparently supposed to have teachings for all the people, all over the universe. Am I right?
Ah..yes (if I understand your question correctly).
I don't get the idea here. WHO are going to elect the rulers and what/who is gonna certify those bolded criteria in the people who are electing the rulers?
Even though it doesn't mention elections (you're assuming it will be an elected government) but for arguments sake...how do we elect our leaders now? How have people elected leaders in the past? Is this a new concept to you? Why do you support Mousavi? He has a history behind him right? He stands for certain things, right? He has promised to make changes, hasn't he? Common.
Well, talking about it seems to be way too easy but point is that HOW are we gonna know this "those" practically?
What do you mean
how? That's our problem isn't it? A lot of countries already fit that criteria already, how did they do it?
It's all beautiful and touching but it's only talk. Even the most unjust governments believe that their economic system is equitable and orderly. I mean these are actually the bare facts, the obvious and initial goals for every government. It's not like Islam has established these basics and it's not like that abandoning these "Islam teachings" is the reason for Islam world being in such turmoil because suggesting practical WAYS and methods in order to reach these goals is what matters at first.
Again, with the "it's only talk", who would you have enforce these?

And not following these basic ideas are ONE of the
major reasons why it is in turmoil you can't deny that. Why is it there peace and tranquility in places they have better economic policies & structure and give their people more rights?
Does it mean that infidels (كافر

are also allowed to live among the other people, benefiting from similar rights?
You need to stop placing beliefs of your fellow citizens or your interpretation of Islam on me. I don't call anyone a kafir. I'm an Ahmadi ffs, I'm labeled as kafir.
And you even asking this question means you haven't understood the fundamental concept of the piece I posted. There will be no religion involved in the government so why would it matter if someone is "kafir" or not?
What religious duties and obligations you mean? For this I think that you first need to tell me how this government is gonna be elected. Now suppose that the majority of a society are electing a government which doesn't oblige itself to carry out religious duties and obligations and the majority also don't care about these duties and obligations. Are Muslim subjects who do care about those duties allowed to disobey the government or even fight with it?
It means that you are to follow the rule and law of the country you live in. That means, I as a US citizen am to follow the law of the land regardless of what I think of it. The only exception being a government that stops you from practicing your religion. The duties and obligations meaning the five daily prayers, reading the Qur'an, or what have you.
No, I don't need to tell you how "this government is gonna be elected" because you clearly didn't understand the piece I posted. It doesn't say or require any one type of government.
OK, so if this society that doesn't want to carry out religious duties and obligations elects a government that doesn't care about these things...will it stop people who do want to?
The government of Pakistan follows a so called Sharia Law that it interprets and bends at its will and in the constitution Ahmadi Muslims are labeled as "non-Muslims". We are not allowed to give out our religious material, we are not allowed to preach, we are not allowed to have mosques, we are not allowed to give the call to prayer, we are not allowed to perform the haj, and after we were declared non-Muslim an extra line was created in Pakistani passports that is labeled "Religion" (the only country in the world that has it that I know of) and there we have to write "Ahmadi" or testify that our prophet was an impostor (Dajjal), even saying "Assalamo Aleikum" is a jailable offense. Yet they cannot, no matter how much they want, stop us from praying and gathering. That is how we stand up to them; we do not fight back and we are involved in any type of sectarian violence.
What if the country A, attacks the country B. Do we have to/are we allowed to recourse to arms in such situation?
You didn't read at all did you?
It clearly says "Recourse to arms is permitted in self-defence only" I don't know clearer it can get.