Yes, "Jazz" should be capitalized because it is a proper noun referring to a specific genre of music.
It should be capitalized if it follows or precedes a name.
No it shouldn't be capitalized.
No, the word "revivalist" does not need to be capitalized unless it is at the beginning of a sentence or part of a proper noun.
yes it needs capitalized.
The word "Godspeed" is usually capitalized, just as the word "God" is usually capitalized.
Yes. It is a proper noun when used as the name of the music. In case it has been a while since you took a grammar course, all proper nouns (nouns that are the name a specific thing) are capitalized. Jazz, County, Rock, Hip hop, Pop, etc., etc.
The word evolution does not need to be capitalized.
No, coral does not need to be capitalized.
No, circa does not need to be capitalized.
No, it shouldn't be capitalized.
No, it doesn't need to be capitalized.
No, kinetic energy doesn't need to be capitalized.
It should be capitalized if it follows or precedes a name.
Yes, the 'A' in AIDS should be capitalized as it stands for Acquired Immunodeficiency Syndrome.
No. Queries do not need to be capitalized.
No it shouldn't be capitalized.
Yes, "Black community" should be capitalized as it is referencing a specific racial or ethnic group.