Yes it should be capitalized.
Yes, America is always capitalized because it is a propernou n.
Yes because it is a proper noun. It is referred to particular group/people that's why it is necessary to write the word 'american' as "Americans".
The word 'will' should be capitalized only when it is a person's name or the first word in a sentence. As a verb or common noun, it should not be capitalized.
The second word should not be capitalized
Yes, Sunday should always be capitalized.
As an abbreviation it should be capitalized.
No, the word "smartphone" should not be capitalized unless it is at the beginning of a sentence.
The word "banker" should not be capitalized unless it is at the beginning of a sentence or part of a title.
No, the word "epitaph" should not be capitalized unless it is at the beginning of a sentence or part of a title.
Yes, Greek should be capitalized.
No it shouldn't be capitalized.
Yes it should be capitalized.