Rare copyright claims, GDPR, assorted harassment/death threats and underage users have all run across my desk and I would expect any community with a measure of success or broad age appeal to encounter all of these eventually. Granted much of this has not been forums per se and my more extended experience is with assisting in larger communities ie, not in an ownership role. Indeed I avoid being the legal point person at scale because while I can triage any of these I very much don't enjoy being the one on the hook. If you're more obscure or plain small or have a select, chill community most of these perhaps will never happen.
You'll come across these with a wide or lower leaning age variance, in communities that may encounter copyright type issues (even modding is one sticky subject even if it's less likely to be a legal issue for you per se), and places with high passion/volatility which may go as far as well, illegal behavior. Oh and I've had to smite dox attempts, usually as part of some wider internet grudge. The most intense I've gotten myself into has been reaching out to law enforcement, service providers or schools/the like for the super determined as applicable.
"Dark web" is a vague term for a type of website that is probably obscure, innocuous and not much more likely to have an issue as any other. Of course if it's a site based around illegal activity then yeah, they'll always have to watch their back. Needless to say I don't speak from personal experience there.