If the "society" is all by itself on another planet, maybe it doesn't need a state (although it will get one anyway), but here on planet Earth, a "society" without government will find itself quickly occupied by another government.
Yes. There is something in economics called the tragedy of commons. Where spending on something can have a benefit to a wide segment of society even though those people are not paying for it. The most basic role of government is defense and deterring criminals. Another example is roads. And often it is just too expensive and impractical to collect a toll, or put up a fence with a security guard to charge admission to every public space. In other words, what might be described as "socialism" does have its proper place in certain areas of society and the economy. But of course those on the Left have a very much more expansive view of this. In ancient times there did exist a few small states where one king owned almost everything. So in that situation, I suppose it could be described as a free market economy, since almost everything the king did was to look out for his own commercial interests.
