Short answers, pulled from the story.
Friedrich Nietzsche was a German philosopher and writer who lived from the 15th of October 1844 to the 25th of August 1900. He began his career as a classical philologist and was appointed Professor of Classical Philology at the University of Basel in 1869, at age 24, before turning to philosophy.
Nietzsche meant that scientific developments and the secularization of Europe had metaphorically killed the Abrahamic God, who had served as the basis for meaning and value in the West for more than a thousand years. The phrase appears in several of his works, notably in The Gay Science.
The Übermensch, introduced in Thus Spoke Zarathustra, is the creator of new values who rises above the herd and above the notion of good and evil. Nietzsche presented it as a solution to the problem of the death of God and nihilism, declaring through Zarathustra, "Man is something that shall be overcome."
Nietzsche suffered a mental breakdown on the 3rd of January 1889 in Turin, after which he lost his mental faculties for his remaining 11 years. His insanity was originally diagnosed as tertiary syphilis, but later researchers proposed alternatives including manic-depressive illness with vascular dementia, a meningioma, frontotemporal dementia, CADASIL, and mercury poisoning.
After Nietzsche's death, his sister Elisabeth Förster-Nietzsche became curator and editor of his manuscripts and edited his unpublished writings to fit her German ultranationalist ideology. Through her published editions his work became associated with fascism and Nazism, even though Nietzsche was explicitly opposed to antisemitism and nationalism.
Nietzsche was never married. He proposed to Lou Andreas-Salomé and was rejected each time; she had been interested in him as a friend but not as a husband.
Eternal return, also called eternal recurrence, is the concept that the universe has been recurring and will continue to recur for an infinite number of times. Nietzsche first proposed it in Section 341 of The Gay Science and in the chapter "Of the Vision and the Riddle" in Thus Spoke Zarathustra, considering it potentially horrifying and the heaviest weight imaginable.