Here are the correct responses to the questions you provided:
Question 1: How does weak background radiation coming from every direction in the sky support the Big Bang Theory?
Response: it provides evidence of universe expansion
Question 2: How does the change in the temperature of the universe provide evidence for universe expansion that supports the Big Bang Theory?
Response: The universe is cooling which, according to the Big Bang Theory, is expected to happen as the universe expands.
Question 3: How is dark energy related to the theory of the Big Bang?
Response: It causes the expansion of the universe to accelerate.
Question 4: Which evidence supports the idea that Cosmic Microwave Background radiation is a remnant of the Big Bang?
Response: Its temperature is uniform.
Question 5: Blueshift is observed when
Response: a distant luminous object travels rapidly towards an observer.
Feel free to ask if you have more questions!