Marx was a member of what can be understood as a vanguard party, the International Working Men's Association. Marx was not against vanguard parties. The Paris Commune was a dictatorship of the proletariat, but you're fixating on the key problems with it that prevented it from being a successful dictatorship of the proletariat, which the Bolsheviks succeeded in establishing.

Lenin's point on how, without forming broad working class organizations, sponteniety will at most result in the Trade Union consciousness, is correct. It isn't that the proletariat could not form class consciousness in general, but that without an all-encompassing organization, these will always be limited to the extent that the proletariat is confined to local struggle. Having the most politically advanced among the proletariat organize in a political party is the same as how Marx engaged in political practice.

Lenin did not draw a distinction between the proletariat and the political party. Lenin did the opposite, stating that the party is of the proletariat. "Intellectuals" are not a class, they are a subsection of every class, and in organizing in a political party they serve as proletarian "intellectuals." I'm using air quotes because the term "intellectual" is a social role, not a measure of intelligence, you can be a very stupid intellectual or a very smart non-intellectual.

As for Trotsky/Stalin, this is wrong. Trotsky became a traitor, and was wrong about distrusting the peasantry. Stalin was more correct than Trotsky, and though I would charitably say that their big schism was an avoidable tragedy, Stalin was the one in the right on that fight. That's why he was elected, and supported by the people.

As for Marxism vs. Anarchism, the final end result of each is entirely different. Marxism posits full collectivization across the entire global economy, which represents a true end to class distinctions globally. Anarchism instead goes for full horizontalism, which results in petty bourgeois worker-cooperative style cells. Marxism and Anarchism understand class and the state differently, so what is stateless and classless for a Marxist has a state and class for anarchists, and vice versa.