No, in fact it is the opposite---generally there are not quotes used. However, you would cap and use quotes if it is the name of a book, movie, etc., unless the stylebook calls for italics instead of quotes.
No. You capitalize titles and proper nouns, but you treat a quote as you would any written sentence.
Yes, you always capitalize "Cuban."
Yes, always.
No you do not.
Yes, you capitalize Spanish because it is a language and culture.
Yes, you always capitalize a day of the week.
Yes, always capitalize a state.
Yes, you should always capitalize a proper adjective.
Always. It is a proper noun.
no
Nope!
Euro is always capitalized.