Is the economic system fair to everyone?

Communism: If done exactly as described by Marx, fair but not good. Everyone being equally poor and starving might be fair but it is not a lofty goal to strive for. This is starvation with extra steps.

Socialism: Not fair. Typically socialism requires taking from net producers and giving to net consumers. This implies that I do not own my labor and therefore I do not own myself. This is slavery with extra steps.

Crony capitalism: Not fair. I suspect this is what you mean by “economic system.” This system is fraught with what economists call rent seeking behavior and rewards entities without those entities providing commensurate value to all parties affected causing a negative externality or external cost.

Free market capitalism: The most fair but also potentially the most unequal. Individuals are allowed to use whatever resources they can attain by non-violent means to whatever end they wish. Typically this does not cause as many unresolved negative externalities because of a fear of committing a tort by those who cannot afford to. There will be individuals in this system with very little despite their great effort and desire to be otherwise and there will be others who collect great wealth simply because they will inherit it. 

It is important to remember that if fair is not equal.