Why does the darkness of the night sky lead to the conclusion that the Universe cannot be infinitely big?

For each question, just need few sentences to answer it. These are questions.

Problem 1: Why does the darkness of the night sky lead to the conclusion that the Universe cannot be infinitely big?

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Problem 2: Light cannot come to us from the earliest age of the Universe. How old was the Universe when light began to stream freely, and allow us to observe it? Why was light from before this time trapped?

Problem 3: The light from this age of the early universe can be detected today. What is this light called? Does it come from any specific part of the sky?

Problem 4: The light from the earliest age of the universe is at what wavelengths? Was it always this wavelength? Explain how the wavelength of this light has changed as the universe has expanded.

Problem 5: Although the light is essentially the same wavelength, there are fluctuations of one part in a million or so. What do these fluctuations in the light from the early universe correspond to in today’s universe?