I can't comment on aesthetics, but Marx claimed to be deeply skeptical about ethics and political philosophy. This influenced the culture of Marxist socialists — somewhere G.A. Cohen (a philosopher who was raised in a Marxist community in Montréal) has an anecdote about his uncle saying that he didn't care about justice; he was just looking out for the interests of his class. So before we unpack the notion of "the universal class," we need to unpack Marx's meta-ethical views.
Briefly, remember the idea of the base and superstructure from Marx: the system of production provides the base of society; things like culture, philosophy, and politics are built on top of that superstructure; and the dominant elements of that superstructure generally and for the most part reflect the interests of the class that controls the base, and indeed frequently provide ideological cover for the class structure of the base. So specifically ideas of justice in liberal political philosophy — think Locke, Smith, Bentham, and Mill — reflect the interests of the dominant class in liberal society, namely, capitalists. For example, Adam Smith represents markets as spontaneous developments in the state of nature, made by free and uncoerced human beings. This provides ideological cover for the actual labor markets of nineteenth century Manchester, which in turn makes the conditions of the English working class appear just. Charles Dickens' novel Hard Times shows how Bentham's utilitarianism provides ideological cover for the class system, in the form of Thomas Gradgrind.
There were rivals to liberal political philosophy before they came to be so culturally influential. For example, Locke's major work of political philosophy is the Two Treatises of Government; the First Treatise in this work is an attack on Robert Filmer's argument for hereditary monarchy. On Marx's view, liberal political philosophy came to power (in a cultural sense) not by virtue of being true or having better arguments than their rivals, but instead because of the ideological cover they provided to the rising capitalist system. The changes in the base — industrialization, capitalism, and empire — drove the changes in the superstructure, not vice versa. Similarly, on Marx's view, socialism will replace capitalism not because socialism is just or true or is supported by better arguments, but because of causal laws governing the economic and class development of society over time. This is why Engels called Marxist socialism "scientific socialism": because it puts forward scientific predictions (in some sense) of class dynamics, rather than justifications in terms of morality or justice.
At least explicitly, this view of moral and political philosophy seems to make Marx kind of a moral relativist: there's no one true moral theory, but instead merely the rival moral theories used to rationalize various class structures to the benefit of various classes. From the perspective, the notion that the working class is "the universal class" is nothing more or less than a prediction that a socialist society (a society organized according to the interests of the working class) will be a class-less society. While a socialist society may have different social groups with different interests, there will not be the large inequalities of power between them that drive the development of class societies.
But Marx's language is highly value-laden, and he often seems to work with implicit ideas about morality and justice. For example, "exploitation" is what Bernard Williams' called a thick concept: it has both empirical and normative content. Empirically, Marx identifies exploitation with the appropriation of surplus value in the industrial labor market; the capitalist pays the worker less value than the worker produces for the capitalist in the course of the working day. But normatively, this means that the capitalist takes something from the worker that he (the capitalist) does not deserve. The worker is the one who produced the value; it rightfully belongs to her (the worker). (For more on the implicit ethics in Marxism, I recommend Robert Paul Wolff's Moneybags Must be so Lucky, the introduction to G.A. Cohen's Self-Ownership, Freedom, and Equality, Allen Wood's "The Marxian Critique of Justice" (paywalled), and Norman Geras' "The Controversy about Marx and Justice".)
From this perspective, the notion that the working class is "the universal class" is also (or instead) a normative notion, rooted in universalistic ideas of human equality. On this reading, the interests of the working class are the interests of humanity in general and as a whole; by contrast, the interests of other every class have been specific interests of that class against other rival classes. Capitalist interests were opposed to the interests of late medieval aristocrats, and both were interested in oppressing and exploiting the class of serfs/slaves/workers. By contrast, the industrialized working class (according to Marx's implicit ethical views) has no interest in oppressing or exploiting anyone else. Rather, their interest is in permanently dismantling all forms of injustice.