Another question is how can an anarchist society work surrounded by states and how will it be represented in the international community.
Let me whip out my own shiny pair of crystal balls
Anarchy will happen in one of two ways.
It can happen peacefuly, where anarchists buy or get a piece of land from a country, or set up seasteading ships, and just migrate to the new place. There likely won't be much of a reason to bother or disturb them, since, being uniinhibited by regulations, they may end up having the fastest advancing economy, technology, etc. And they may have enormous wealth and defensive weapons to boot. It would be like countries hating on Google, while all their citizens use it daily. As for how it will be represented in the international community, it will simply be "that place over there. Anarchists don't need representation. If some country wants to enter into deals with anarchists, it would do it on an individual level, such as "this person in particular will provide us with X in exchange for Y."
OR
It can happen violently, where the advent of cryptocurrencies and totally anonymous transactions and business interraction makes collecting taxes and tracking exchanges impossible. Governments will become more violent as they attampt to catch tax dodgers, but will have less and less tax revenues to pay for that violence. Eventually, they will simply collapse from lack of funds. In the mean time, all the austerity measures will make everyone who was depending on governments for medical services, retirement pensions, and wheveter else, will become rather angry at "the system" that has taken their comfortable lives away, and will likely lash out at anyone they percieve to be responsible. This could be wealthy people and businesses, who have money but are not sharing it "fairly" by avoiding taxes, or cryptocurrency and anonymity system developers who are making such a system possible in the first place. In the end, with violence and war simply being too costly, we will end up with regions that don't have government because it would have to be entirely voluntary and without power, and people would just form social and business groups with common interests and goals, but no actual ruling leaders. Whichever states manage to survive will likely only be able to do it through extreme totalitarian powers, such as North Korea or extremely religious violent countries of the Middle East. Some anarchist groups will deal with them, others won't, but there won't be a need for representation, because likely the anarchist group will, again, have way more to offer to those entrenched countries, than they will have to offer to the anarchists.
Find and read The Diamond Age, and maybe Snowcrash, by Neil Stephenson. That's more or less the world that is being build here, right in front of your eyes.