You're way off on your classical liberalism description. There's no-one that considers any form of liberalism as an extreme-right ideology. All forms of liberalism drift around the center despite variations from country to country. In America and Britain they're center-left, whereas Germany and Australia's liberals are center-right. But I don't know a single liberal party in the world that considers itself hard right.
I've seen a variety of two dimensional political spectra, with differing ideas for x and y axis. I would argue for x = economic policy, y = social policy and a third dimension to represent foreign policy. Historically foreign policy is more significant in measuring political positions in the left v right spectrum. Nationalism and foreign skepticism are consistently associated with traditional right-wing ideology, far more than economic libertarianism. Fascism, for instance, is economically closer to communism than conservatism.
As I tried to clarify in the parentheses after my classical liberalism description, 'extreme right' was meant to refer strictly to economic policy. I realize the term has a pejorative connotation and is usually used to describe an ideology that is socially authoritarian and either statist or corporatist economically, but I was only meaning to place classical liberalism on an economic spectrum (I agree that classical liberalism is absolutely not
an extreme-right ideology when factoring in non-economic considerations). If communism is statist and extreme-left, I'd put classical liberalism as the purest alternative to communism (economically) and thus anti-statist and extreme-right. Doctrinaire classical liberals usually favor reducing taxation, spending and regulation to an absolute minimum, a position I characterize as far right as you can get economically. Liberals who favor some amount of government would be better described as social liberals and if they primarily are concerned with using government to protect the environment, blue greens. Also, the term 'liberal' is massively abused outside Europe. American liberals are generally social democrats/social liberals in practice (Obama being closer to a social democrat, Bill Clinton closer to a social liberal) and liberals in Australia are essentially conservatives (John Howard being a good recent example).
I agree that foreign policy is very important in properly classifying ideologies but I don't think it fits well on a left-right spectrum, which I'd reserve exclusively for economic policy. Nationalism appeals to essentially every economic ideology, with slight exceptions for some socially libertarian leftists and some anti-statist rightists (Austrian school classical liberals, like Ron Paul in the US, are frequently cool on military nationalism). I agree that conservatism is strongly associated with nationalism (something that helps differentiate it from classical liberalism) and that fascism can be placed parallel to communism on an economic spectrum. Like green politics, fascism is hard to peg economically; it can be either statist or corporatist. The one economic ideology that has minimal overlap with any form of fascism is pure classical liberalism.