As for understanding the labor theory of value and exploitation theory, this is a good start: http://www.pbs.org/wgbh/commandingheights/shared/minitext/ess_marxsanalysis.html. This is interesting too: https://mises.org/journals/jls/5_1/5_1_6.pdf, but more on the historical aspects of how Marxism is wrong economically and failed in history. And check this out. Here is the Marxism materials list. Of course there’s always google and wikipedia. And there is a lot of good material on this place, you can search this site via google by adding site:mises.org to your search.
Your second question, how putting the state in charge of everything will lead to a stateless society, is one I still ask myself. As far as I can tell, they are just wrong. Marxists say that once central planning has lead to superabundance, the state will wither away on itself. So their theory is statist in practice, but they award themselves a honorary anti-statist label for the intention of creating a stateless society in the end. The problem is that their theory is nonsense. Marxian statelessness fails along with their economics, which does not produce superabundance but starvation. So in reality Marxism is just statist.
I would advise you to not take Marxism too seriously. It is not a meaningful, thought-out economic theory like Austrian or Keynesian economics, but rather a semi-incoherent and often inconsistent mess of ramblings that happen to appeal to the intuitive superstitions of caveman psychology. Marxism was pretty much refuted by the time it was published, and it is generally very anti-intellectual and ignores the facts. The only reason they still stick with their objective value theories, which were refuted a century ago by the marginal revolution, is that without it their entire framework would fall apart.