The first question is simple, fascism as a term derives from the fasces, which were a bundle of rods and an axe carried by lictors to symbolize the power of the ancient Roman magistrates over life and death.

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The second question, however, is problematic. Collectivism and individualism are almost meaningless terms and draw differences that at best only touch the surface of the question you're asking.

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Fascism is a far-right movement because it advocates for an anti-democratic top-down rule of the powerful over the powerless. Yes, Nazis included the term 'socialism' in their name and advocated for this in order to appeal to a mass audience. However, all the influential die-hard socialists were purged from their party in the Night of the Long Knives. There is no sense in affiliating the Nazis with the 'left', if by 'left' we mean a strongly democratic system wherein elected representatives have the power and the ability to tax the rich and redistribute this wealth. Fasicsts practiced no leftism of this sort whatsoever, in fact rolling back government regulations and encouraging big business to form even more powerful syndicates to better compete in the global market.

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The classic 'liberal democracy' wherein elected representatives are limited to voting on political issues is and was the most common system of government in the West. The people in these democracies do not have much power to tax the rich and redistribute the wealth, by design, and today this is still the most popular system in the West. Often this is called 'neoliberalism' as many of the socialist and progressive institutions of the past century are rolled back or privatized.

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Today we often identify 'the left' as those who simply advocate for political rights such as gay marriage or abortion, but that is a bit of a mistake. The 'culture wars' are the battleground that classic liberal thinkers wanted to use to contain democracy so that it would not interfere with the property rights of the very rich. However, fascists were (and are) so far to the right that they totally eliminated even this limited kind of democracy altogether. This wasn't because they wanted to tax the rich and redistribute the wealth, but it was because they believed that the powerful had a right to power and that democracy only weakened a nation.

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The idea that Fascists might be leftists or have more in common with communists than liberal democrats is a popular misconception which has very little substance going for it. One can pick and choose a few facts and draw this picture, but that's very misleading and often serves to justify classic liberalism as a triumphalist ideology. A great piece of historiography that makes this argument in incredible detail is Ishay Landa's the Sorceror's Apprentice.

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