Don’t capitalize an article (a, an, the) when it’s not the first word of a sentence or of the title of a book, movie, etc.
The first sentence in the example is compound, so it need a comma before the conjunction and.
Predate is not hyphenated.
They are known as the Old Ones, and they predate the coming of Man. Where they come from and why they visit is a mystery.
Why is there no comma in the second sentence? Why does it say is a mystery rather than are a mystery? So glad you asked… Flip the sentence around: It is a mystery where they come from and why they visit. That makes sense, right? However, if you’d written, It are a mystery where they come from… That is obviously not correct. Of course, you could also change the sentence to, Where they come from and why they visit are mysteries (notice the change in noun: mysteries, plural), and thus avoid the issue.
When referring to the human species, Man is often capitalized for clarity. (I know it’s generally not considered appropriate these days to refer to humankind as mankind, but this example has a sort of pseudo-Lovecraftian vibe anyway.)