Really depends on the fascist. Like, the Nazi's would be considered centrists by American standards, but they were right wing by German Standards. Fascism can be either right wing or left. Authoritarian all the way, however.
"Human kindness has never weakened the stamina or softened the fiber of a free people. A nation does not have to be cruel to be tough."
In my book, "the Left" means "proponents of government control over economic activities and society at large". The Stalinists being the ultimate "far Left": using our weird contemporary language, "extremely liberal economically, extremely conservative socially". The Nazis were a bit milder on the economic side, and the Fascists substantially less aggressive on both counts, but all three ideologies sit squarely in the "advanced Left" corner.
Otherwise I agree.
Corporatism is entirely consistent with the ideology of statism. You agree that governments should have such power to sell in the first place, I do not.
I don't really see fascism as being either, but it really depends on how you define the two axes (i.e. more right wing or more left wing in terms of what, exactly). Descriptions of political philosophy along a one dimensional continuum is only useful to a certain extent.