Darwinism insists that a family of creatures will evolve over generations to adapt to its surroundings. This is done by the strongest and healthiest creatures surviving longer and breeding more. Marxism suggests that capitalism is the unevolved form of government. This form will eventually give way to socialism out of necessity. Those countries that cling to capitalism without evolution will eventually fail. The natural progression of the evolution beyond socialism is communism. This is the same theory. In both Marxism and Darwinism, the strong survive because their evolution has allowed them to survive in a world where capitalism couldn't.
Yes, Marxism is compatible with Darwinism, because neither of them have belief in the individual as a person. In Marxism, a person is insignificant because they are a slave to the state. In Darwinism, a person is insignificant because they do not exist intentionally. As belief systems, Marxism and Darwinism are compatible in that they both reject the individual.
Marxism is about the abolition of class hierarchy. Darwinism describes how nature constructs classes and hierarchies. One is about building hierarchy while the other one is about destroying hierarchy. It is impossible to be a consistent Marxist and believe in Darwinism.
Marxism is about the strong looking after the of weak in society. Darwinism is about survival of the fitness. You can't have it both ways.
I do not believe Marxism and Darwinism are comparable, but I would assume they could survive in the same setting. Marxism is generally a term involving how a government and economy function, while Darwinism is concerned with sciences and more specifically biology. Scientific thought would be important in a Marxist set up.
Marxism is not compatible with Darwinism. Marxism takes great care to love thy neighbor and his success as much as we love our own. Darwinism believes that the most successful neighbor aims to take all for himself if he is capable of doing so. There is, however, a reasonable balance between these two where society should exist in.
Marxism and Darwinism are not even the same thing. Marxism was a political belief on how a society should live in regards to financial means and distribution. Darwinism is a scientific belief on the beginning of life. I don't even know how people can try to relate two such different subject matters.