Does a UUID that passes validation actually exist in some database?
Not necessarily, and that is the core limitation of any format validator. It confirms the string has 32 hex digits and 4 hyphens in the right positions, at most that the version and variant make sense. It never confirms that specific value was ever generated, exists in a table or matches a real record: that requires a lookup, not a format check.
Is the Nil UUID (all zero) a bug if it shows up in a system?
It depends on the context. RFC 9562 reserves the value 00000000-0000-0000-0000-000000000000 precisely to represent "no UUID" explicitly, so finding it in an optional field can be intentional. It is suspicious when it shows up where a real unique identifier was expected, because real generators (random v4, timestamp-based v7) have negligible odds of producing all zero by chance.
Why does the version sit at the 13th character and nowhere else?
Because RFC 9562 fixed that position from the first specification (RFC 4122): counting the 32 hexadecimal digits without the hyphens, the 13th is always the first character of the third group of 4. Fixing the position, instead of leaving it variable, is what lets any parser read the version without having to decode the whole UUID first.