This is question that requires opionions. Therefore, there is no "definitive" answer.
If you'd like to touch on the subject, please DISCUSS it.
There is no proper answer to your question because it is an opinion. You should consider changing the question to : Who do you think is better looking, Ryan Seacrest or James Franco?
yes they should
American should always be capitalized but not the child. It should be- America n child
No they should not
An American bobtail cat should be groomed at least twice a week.
Yes, "White American" should be capitalized in an essay as it is a proper noun.
No, but you should capitalize American. If the specific branch of the military is named, it should be capitalized.
Yes, the "A" in American should be capitalized when referring to the nationality or cultural aspects of the United States. So it should be "American customs."
Yes, "American Revolution" should be capitalized as it is a proper noun referring to a specific historical event.
The American flag should be flown above a light as a sign of respect
Yes they should
you should explain to her that you are uncomfortable with this and if you find that she is a racist you should dump her :P