Because there are several questions here, this response will focus on the first three, which are most closely connected to each other and to the text in question—The Communist Manifesto. In short, Marx and Engels indeed argue that "the history of all hitherto existing society is the history of class struggles." They define a class in terms of its relationship to the means of production. Because productive forces change over time, classes change over time:
Freeman and slave, patrician and plebeian, lord and serf, guild-master and journeyman, in a word, oppressor and oppressed, stood in constant opposition to one another, carried on an uninterrupted, now hidden, now open fight, a fight that each time ended, either in a revolutionary reconstitution of society at large, or in the common ruin of the contending classes.
In short, the driving force behind history itself was conflict between social classes that were inextricably tied to economic forces. In the past, these social classes were complex and large in number. In medieval Europe, for example, Marx and Engels see multiple classes, including "feudal lords, vassals, guild-masters, journeymen, apprentices, [and] serfs," each of which had specific interests based on its economic situation and its relationship to other classes. Conflict between these classes, as Marx and Engels argued in the long sentence quoted above, led to major social change that often included their destruction or "reconstitution." Even if they didn't realize it, they were struggling, ultimately, for control of the means of production.
By the mid-nineteenth century, the rise of industrial capitalism had simplified this conflict, creating two classes. The first was the bourgeoisie, which essentially included business owners, and the second was the proletariat, the industrial working class created by the rise of industry. Marx and Engels argued that these classes were locked in permanent conflict, one that would inevitably terminate with the destruction of the bourgeoisie and the advent of a classless society—communism. The authors reasoned that industrialization, with its obsession with rationalization and efficiency, would result in a larger and larger working class that was increasingly alienated from the value of the goods they labored to produce. In short, the bourgeoisie would lose because in revolutionizing the means of production, it produced, as Marx and Engels memorably wrote, "its own grave-diggers."
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In Chapter 1, titled "Bourgeois and Proletarians" of Karl Marx and Friedrich Engels's The Communist Manifesto, both authors make it very clear that the two struggling, or even battling, classes are the bourgeoisie and the proletariat. Marx defines the bourgeoisie as the ruling middle class; the class that owns land, capital, and is responsible for both production and employment--they are essentially the business owning class (Encyclopedia of Marxism: Glossary of Terms, "Bourgeoisie"). The proletariat is the lowest social class; the members of the class are specifically the people who work for the bourgeoisie for wages as opposed to a salary income. Based on Marx's definition, the proletariat generally live in poverty and are subordinate to the bourgeoisie. In this first chapter, Marx and Engels describe the class struggle as a struggle of the oppressed against the oppressors. They argue that the fight is sometimes open and sometimes hidden but always leads to either social reconstruction or to destruction of both classes. The struggles of both classes are essentially a struggle for more prosperity and more equality.
Marx and Engels argue that, no, it has not always been the same two classes struggling, but the reason for the struggles has always been the same--oppression. Marx and Engels use the following sentences to describe the class divisions and struggles throughout history:
In earlier epochs of history, we find almost everywhere a complicated arrangement of society into various orders, a manifold gradation of social rank. In ancient Rome we have the patricians, knights, plebeians, slaves; in the Middle Ages, feudal lords, vassals, guild-masters, journeymen, apprentices, serfs; in almost all of these classes, again, subordinate gradations. (Ch. 1)
More specifically, the bourgeoisie sprang from the surfs in their struggle against the feudal system. Feudal lords were the land-owning members of the aristocracy who rented their land to serfs to live on in exchange for the serfs' labor, especially agriculture labor. The serfs would work the land for their own food but pay the majority to the lord. New commerce markets, especially in colonized America, led to a death of feudalism because the manufacturing middle class now earned far more money than feudalism could acquire. As modern industry began to develop, society began to be divided into those who owned industry and those who worked the industry.
Marx and Engels further argue that it will be the proletariat who will win the current class struggle, mostly because the actions of the bourgeoisie is leading to the destruction of its own class. The mass production of the bourgeoisie leads to one major problem--over production. Over production diminishes product value. Marx and Engels argues that there are only two possible solutions to over production: (1) by eliminating mass production or (2) by developing new markets, which will render the old markets useful again and re-establish value. The bourgeoisie is too addicted to monetary gain to want to eliminate mass production completely, so it will continue to develop new markets and even colonize to create new markets. In doing so, the bourgeoisie becomes ruled by production, making the bourgeoisie no longer the ruling class. What's more, industrialization cannot exist without the laborers. As the bourgeoisie strive to open more and more markets and produce more and more goods, the class needs more and more laborers. But the problem is that the longer a laborer works as a laborer, the more he/she sinks into poverty, or as Marx and Engels phrase it, "sinks deeper and deeper below the conditions of existence of his own class" (Ch. 1). The deeper the bourgeoisie lets the proletariat class slip into poverty, the more the bourgeoisie proves it is not fit to rule because it cannot "assure an existence to its slave within his slavery," and the demise of the proletariat will of course lead to the destruction of the bourgeoisie (Ch. 1). Hence, the proletariat becomes the winning class in the struggle because the bourgeoisie is becoming more and more oppressed by its own powers of production, leading to the demise of the one class needed to maintain production--the proletariat.