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.
Jazz is generally always capitalized.
No. Jazz is an informal noun.
You should capitalize it if it is a brand name.
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
It should not be capitalized.
No
Yes you should capitalize the name of cities. You would capitalize it because it is a proper noun.
Yes, you should capitalize the C in Century.
You should capitalize it if it is a brand name.
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
Yes, you should capitalize "The Rotunda" as it is a specific place or location.
You should capitalize Colosseum when referring to the specific ancient Roman amphitheater in Rome.
It should not be capitalized.
No
no
No
The words The Jazz Singer should be in italics.
Yes, it is correct to capitalize "Should" if it is used in a title as it is a noun in this context.
You should capitalize "Musical Theatre" when referencing the specific genre or art form.