Final answer:
The correct use of a colon in multiple choice question 1 is option C, and for question 2, sentence A requires a colon before the list of dishes.
Step-by-step explanation:
For your first question, the correct answer is option C. We considered the following name for our cat: Smokey, Oscar, and Sock Thief. The colon is used correctly here because it comes after an independent clause and introduces a list directly related to that clause, which is the list of names being considered for the cat.
For your second question, sentence A requires the use of a colon. It should be written as I sampled various dishes: shrimp dumplings, steamed pork buns, and rolled rice noodles. The colon is required after 'dishes' to introduce the list of foods sampled.