What does the “overman” represent ? What way of life does this figure signal and try to teach us about today? How would the overman’s point of view represent a difference from Platonism and Christianity?

Response to this thread does absolutely not need to answer all of my questions!
Remember to post a contribution of at least 200 words.
Questions on Nietzsche’s Thus Spoke Zarathustra:
1. Nietzsche, we could say, even though he represents an atheistic point of view, agrees with Plato and Augustine in the basic characterization of a two-world metaphysics. In what way does Nietzsche follow their characterization of this form of thought? How does he also represent a critique of two-world metaphysics?
2. Explain the metaphorical meaning of the three main symbols in section 1 of Thus Spoke Zarathustra, especially as these symbols relate to metaphysics, Plato, and Christianity: The cave, going under, and the sun.
3. Zarathustra encounters an “old saint” in section 2. What point of view does the old saint represent, and how does Zarathustra depart from or dispute that point of view? And, most importantly, what does Zarathustra mean when he says, with reference to his conversation with the old saint, “God is dead!”?
4. What does the “overman” represent ? What way of life does this figure signal and try to teach us about today? How would the overman’s point of view represent a difference from Platonism and Christianity? Why can we call the point of view of the overman, his adherence to “the meaning of the earth” , something like what is sometimes referred to as existentialism?
5. Do you agree with Nietzsche’s basic characterization of Christianity as implying hatred of life ? Why or why not?