no
Yes you should.
The pronoun "I" should always be capitalized.
Yes, you should capitalize "About" in a title.
Yes it should be capitalized. Remember to follow the punctuation that the company in question uses.
Yes, you should capitalize the C in Century.
Yes, always capitalize American because it is a proper nou n.
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 be--- The first paper asked the question, " Why attend such a conference?" with the answer, "Connections."
You should capitalize Colosseum when referring to the specific ancient Roman amphitheater in Rome.
Yes, you should capitalize "The Rotunda" as it is a specific place or location.
It should be--- The first paper asked the question, "Why attend such a conference?" with the answer, "Connections."
It should be--- The first paper asked the question, " Why attend such a conference?" with the answer, "Connections."