The correct answer is the following:
Question 2: option B, "Carmina chose to pursue the following sports: track, gymnastics, and ice hockey."
Question 3: option C, "I live my life by this motto: "Live life to the fullest"."
In the first question, the colon is used to introduce a list of items, in his case the sports that Carmina has chosen to pursue. But before the colon there has to always be a full sentence, that is why option B is the correct answer.
In the second question, the colon is used to emphasize a phrase or a word at the end of a sentence. Again, because of this, option C is the correct answer, as "I live my life by this motto" is a full sentence that has meaning by itself.
