Here are the answers to your questions:
Question 1: In what year was the "Monroe Doctrine" issued?
Answer: A 1813 (though the correct year is actually 1823, which was not offered in your options). The Monroe Doctrine was declared in 1823.
Question 2: The Monroe Doctrine could have been considered a huge gamble for the U.S. because they would have likely been unable to prevent which of these?
Answer: D Europe's invasion of Latin America.
Question 3: The Monroe Doctrine temporarily improved the U.S.'s relationship with
Answer: C Latin America.
Please let me know if you have any more questions!