While ethics are used for justifications, that doesn't mean you can have an intelligent discussion about justifications.  What this would end up being is a back-and-forth about whether something is or isn't.

What any intelligent discussion on this topic will be about will NOT be about justification.  It will be about the finer details themselves, which also somewhat disappears when there's no real defined state.  Not everyone agrees on what constitutes a state.  There is, at some point, a blurry line between state and non-state actors.  That, in my opinion, becomes the second problem when trying to talk about this topic intellectually.  

What are we using as the basis for defining a state?  This quote from your OP is the reason why it's hard to even give an intelligent answer to the question in the OP to begin with.

"So my question is: how do states form, who is able to form them, and why do they represent the opinion of all individuals residing in a land, not only at the time of creation, but for generations afterwards? "

I'm thinking maybe your question really isn't about states themselves, but more about governments in general. 

We don't need a unified definition of a state. The question pertained to one's personal justification for one's specific concept of the state. The purpose of this thread was to spark a sharing of ideas in regards to why states "should" exist. In order to explain why they "should" exist, one must appeal to some form of ethics. This is all intellectual, because it is the first step in determing differences between political ideologies. That is useful, because it allows one to frame all other political arguments from one's knowledge of the underlying ethics beneath this political question. 

http://en.wikipedia.org/wiki/Justification_for_the_state#Political_ideologies

There is no single, universally accepted justification of the state. In fact, anarchists believe that there is no justification for the state at all, and that human societies would be better off without it. However, most political ideologies have their own justifications, and thus their own vision of what constitutes a legitimate state. Indeed, a person's opinions regarding the role of government often determine the rest of their political ideology. Thus, discrepancy of opinion in a wide array of political matters is often directly traceable back to a discrepancy of opinion in the justification for the state.

I do have to admit that the question was poorly phrased. Let me refine it

"So my question is: how do states form, who is able to form them, and why should they be formed and continually exist."

Well, you've got me over a barrel in the first point, kudos. It's not a state since it's formed on an ad-hoc basis.

Second point, though, i would still contend goes my way. We're talking about a society composed almost entirely of free farmers, maybe some fishers and shaman. Could, for instance, entities like large corporations function fairly in such a system of pure voluntary associations? Equally, the trouble of paying for justice is that, contrary to the claims of your Icelandic example, is that it would result in virtual slavery for the poor (work to pay off judgments against you), especially when the question of voluntary association weighs the playing field in favor of the rich. It would quickly become open to mass violations of individual liberties through inequality of opportunity. Especially as the wealthy would have much more buying power for these voluntary, private courts, diminishing accountability in that regard (something which would open the door to large-scale corruption in these groups as well).

This things functioned in a low volume society of small producers. It is very difficult to "test" how the rigors of capitalism would have upended it, but history showed that the small producers were the main victims of capitalism's rise.

But the problem I have with that is say we make a contract to make 1,000,000 burgers and so to fulfill the contract I need to buy 500 steers more than I have. Then you cancel when I have the steers and now I have 1000 steers that I can't sell to anyone.

How is that then enforceable by law? Who satisfies me upon your breach?

It wouldn't result in slavery for the poor as the value of the enforcement of their right is the same as it is for the rich. Their reward is not payment from the rich, but payment from the enforcement of the right (retributive.) They make a decision to buy this right off anybody, the poor/rich, etc. Then it becomes their responsibility to bring the aggressor to justice, as it is in their self-interest (profit-wise) to do so. If the rich harm the poor, that is more incentive for the agency to take that case because it means a larger reward in the instance that they win.  Yes, the rich might bribe them or pay them, but that happens with a state enforcing public law as well. We can say for certain that large corporations don't function fairly with the state, so it's a reality regardless of the state's existence, and honestly if a company wants to maximize its profits in the business it will target all consumers: rich and poor. 

I'd argue that history shows  small producers were the main victims of the state's involvement in economic activity. Almost all long-lasting monopolies and unfairness which were in favor of large business have been at least partly due to the hand of the state. For every monopoly you name there is a bill, regulation, or judgement that enabled it. Lysander Spooner and Benjamin Tucker, 19th century individualist anarchists and leftists, both of whom subscribed to socialist/marxist analysis, believed the poor were in the predicament to sell their labor only because the state made it impossible for them to otherwise through various credit and fiscal regulations. Lysander Spooner also believed in natural rights. So that is an interesting bridge between marxism and the pre-existing liberalism. 

That was a huge risk you made. There was no way you could confirm whether or not the other party was even able to provide you with 1,000,000 burgers. What if their business was on the brink of collapse and crashed right after you made the contract? But let's assume it was a reasonable economic decision and you make your case. By claiming that the other party must provide you with 1,000,000 burgers, you are claiming ownership of that/those person(s.) They are your indentured servants until they provide to you burgers or the equivalent thereof. That can't be the case though, because we are born as owners of ourselves and can't transfer ownership over ourselves to others. So legally, unless you believe slavery/indentured servitude is morally justifiable, there is no case to enforce that contract. Yes, you are out of luck because of your poor decision, but that doesn't give you the right to enslave another human being or group of human beings for a period of time because of a promise they'd made to you. If this were true, then all people who sell their labor would be enslaved by their employers because they can't break their end of the contract whenver they wish to. 

That just seems really unfair. As someone who comes from poverty, this makes me feel powerless against people who have everything already

I don't know why. Personally, self ownership and liberty make me feel more powerful. To say that nobody owns me and nobody except I can use and choose my own path, well that is quite nice, in my opinion. And seeing as I've come from the bottom of poverty (was homeless for 6 months during my childhood) that doesn't change a thing. If anything, legally binding contracts that are not rooted in property rights help the rich and hurt the poor (i.e concessions on labor rights, price-fixing, monopolies, etc, etc.) 

I really don't see why you should be able to legally-bind promises. If that were the standard way of doing things, people would be able to sue for entitlements that they don't deserve (if I promise to get my brother a car, and decide not to, he can sue me - for example.) Contracts are entirely rooted in property rights (as are all rights.) 

but that's a promise, not a contract.

The way I look at it, I could work my whole life building up a business and in an instant have it destroyed by some company who simply decides they don't care about fulfilling their obligations.

I don't understand your criticism either. How is it that we have both enforceable contracts and at-will employment? The way you talk it sounds like the two shouldn't co-exist.

Isn't your version of a contract a legally binding promise? If that were the case, then all promises can be perceived as oral contracts. What distinguishes a contract (in your view) from a promise? 

Why would you give somebody (or bodies) that much power over your business in the first place? Any good business doesn't depend on a single trade partner so much that it would be devastated by a separation from that trade partner. If your business fails because of something like that then it fits well with the nature of the competitive market, we need both profit and losses for the system to work, and smart decisions should be profitable and poor decisions unprofitable. Just because you're a small guy or poor doesn't mean you should get special priveleges, just the same priveleges. Same is true for big companies, there should be no such thing as "too big to fail." 

The reason why we have contracts and people can terminate their employment is because labor contracts are precisely recognized for what they are, promises, and they are unenforceable. A worker is recognized to have a right to quit, regardless of what his/her contract was, just like an employer is recognized to have the right to fire. This has not always been the case though. Indentured servitude was a real thing. Contracts can get in the way of wage bargaining though. For example, if there is a stipulation in the contract, a company can refuse to pay the employee the accepted rate (and this is entirely "contractual.") That is theft of the other participant's labor. Another example of a bogus contract that hurts consumers is the termination fee one pays the phone or cable company. One should be able to secede from any agreement upon one's choice and not be extorted. 

Also, you seem confused. I never argued that the existance of enforceable contracts contradicts at-will employment. I argued that contracts which codify a promise are not enforceable. Only contracts grounded in property rights are enforceable.