American is a proper noun. It can also be an adjective, as in "American cheese." A rule of thumb: proper nouns are capitalized and common nouns are not capitalized.
Yes. The word American is always capitalized in English, as are other nationality adjectives. Although a case could be made for "American cheese" if "french fries" is lowercased.
Fontina should be capitalized but not cheese.
Yes because it is a specific type of cheese.
They are not proper nouns. They would not be capitalized in a sentence.
Yes, only the proper name "Swiss" is capitalized; cheese is a common noun.
Yes it should be capitalized.
Yes, the Mozzerella should be, the "cheese" needn't be.
Yes, "Gorgonzola" should be capitalized because it is a proper noun referring to a specific type of cheese named after the town of Gorgonzola in Italy.
Yes, "Swiss cheese" is typically capitalized because Swiss refers to the type of cheese rather than the country.
You just did. -I think all cheese names should be capitalized
Yes, if it a subject called American History. Otherwise, just American is capitalized.