I can answer the second part of this question, but not the first (sorry!). The claim that 'everything happens for a reason' is known as the Principle of Sufficient Reason. It is commonly associated with Leibniz (and before him, Spinoza), but played an important role in German idealism, and was the topic of Schopenhauer's doctoral dissertation. You can find the references for these and other discussions in this article from the Stanford Encyclopedia:
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In which book, which chapters does Hegel talk about 'everything happens for a reason'? Are there other authors that talk about this topic? What are the titles?