Marx believed that society, politics and economics were subject to inevitable forces that would cause change. (Dialectical Materialism for those of you who have too much time and too much sanity). Loosely speaking, Marx believed in a form of social evolution.
Marx also believed that "class" was a useful framework for analyzing society - by analyzing the class interests, you could determine the political viewpoint and agenda of individuals. He believed that the proletariat shared a common interest and the Bourgeois shared a common interest, and that the class interests were more important than any other tie between individuals. Race, gender, sports teams, sexuality, etc were all irrelevant because the proletariat's class interest was the only useful predictor of politics.
The status quo was bourgeois oppression - wealth was in the hands of the bourgeois class and the primary interest of that class was oppression of the bourgeois (*update: user4581 is correct, it would be more precise to say that the primary interest was to oppress the proletariat in order to maintain the supremacy of the bourgeois; I find that level of precision rare). Apparently if you have wealth, you lose interest in sex, sports, food and drink in favor of the joy of oppression.
According to Marx's historical viewpoint the status quo - bourgeois oppression - would inevitably give way to a socialist revolution. Once the bourgeois were overthrown, then all of mankind would recognize their essential brotherhood. Manchester United Fans would root for Liverpool and vice versa because everyone would be a proletariat, everyone would be equal and everyone would be happy. Once you dispose of the Bourgeois, there is no longer any need for class.
1) It should be obvious to anyone who has read any of my answers that I don't have a lot of respect for Marxist economic theory. It simply doesn't describe any reality in which I've ever lived.
2) I don't have any good resources to recommend; partly because of (1) and partly because OP is asking for an explanation which is rather difficult. Yahoo does a decent job, but I think the fundamental problem is bending your mind to all the assumptions that Marx held and which are no longer tenable.
3) A potentially useful reference is Revolutions Podcast 3.1 - the first five minutes don't answer the question, but I think they help to clarify the process of understanding Marxist history.