Answer: True
Claims is the statement that gives the answer or conclusion to a question or problem.
In a good paragraph, all the sentences refer to the main idea of the paragraph. So if the topic sentence refers to the main idea of the paragraph, the remaining should too (false).
I believe you have a typo when it comes to the first option - it should be athletics, not athletic. The word athletic is an adjective, and the word athletics is a noun.
That being said, the correct answer is A. athletics. Even though this noun ends in -s, it is still singular. The rest of the options are all plural nouns.