No it isn't. The market economy requires common defense, contract enforcement, fraud protection and a few other basics to work at all.Not really, under a modern market economy anarchism is quite possible.
Which is why Anarcho-Capitalism is only a fantasy. Human beings don't follow those principles, especially the non-aggression principle.Anarcho-capitalism does not need coercive force of any kind because it is based on the contractual society, the right of self ownership, and the non-aggression principle.
No, it was what anarchy inevitably turns into. The anarcho-communists had the same absurd idealistic notions you share that everyone would just work together and so no government was needed at all. They realized that didn't work, and compromised their beliefs by allowing votes into the workers councils.Mob rule =/= anarchy in any way, shape, or form.