[etplayer]

>Capitalism is inseparable from a free market system.

No, it's not; there exists market Socialism, for example. There also exists mutualism. I don't know where you're getting this from other than the idea that authors in favour of capitalism also tend to prefer free market economics.

>Whether we're talking rudimentary Socialism or its derivatives, including Fascism and Communism.

Communism is actually the complete lack of state control but also the lack of commodity production and therefore the market.

>Regulation is antithesis to Capitalism because it imposes State control over the economy.

You have still failed to explain why lack of regulation is central to capitalism other than to name Hayek, Mises and Friedman who were in favour of free-market capitalism. Other authors who sought to describe capitalism prior to them didn't include "free market" as a core principle of capitalism.

There is no denying that the epitome of capitalist production is completely unencumbered by a State, but there is also no denying that the state must intervene in a capitalist economy to protect property rights on a large scale. There is also the idea that the the State itself cannot be a capitalist actor which is totally false; we see the State engaging in the employment of wage-labour and selling on the national and international market. This makes the state as capitalist as Microsoft or Google.