Individuals, and individual rights, are like single atoms. They only exist in the abstract sense. The real world is entirely dominated by groups and collective actions.
You're a confused anarchist. The problem with non-coercive government is that all government is coercive. Government is primarily a set of restrictions on the use of force, or alternately the monopoly on that use of force. Getting rid of a government, or disarming it, merely allows anyone with a larger arsenal to set up their own government -- anarchy is an unstable system. We all have a right to violence, because it cannot be taken from us except in extreme situations. Remember, the Code of Hammurabi was instituted, "...so that the strong might not harm the weak." Coercive government is a necessary evil, and it will remain necessary so long as men are capable of harming their fellows, for that is its justification and primary purpose.
Rights are not inherent, except in some abstract sense. In the real world, your rights are what the men with guns say they are. You may feel fortunate that the world has had a long, bloody time to work out semi-cooperative frameworks to restrain our darker impulses. Individual rights are an important conceptual counterbalance to the overwhelming powers of the collective, but they are no justification for anarchy, economic or otherwise. The "free market" is an ideal, even a good one, but in most cases removing government interference makes markets less free, more subject to collusion and fraud. In some cases, where the service is required to be universal, or when the barriers to entry would be insurmountable, it makes sense for the government to assume these functions directly. Govenment can also be thought of as the natural monopoly of natural monopolies, in that sense.
Slavery is a word that has a specific meaning; your definition is specious. You just fundamentally don't like being told what to do. To some degree this idealism is admirable. For the true individualist, I can recommend (from long personal experience) the Alaskan wilderness; you can get land for free still up there, provided you build upon it. Whatever romantic images your mind conjures upon thinking of Alaska are all true; I can't stand the weather, personally, but it's as close to a pure state of nature as you will ever find. If you'd like to enjoy the benefits of society, however, you have to play by the rules. "Slavery" isn't an option -- it's mandatory.