In this case, I imagine "monetize" actually means "at least earn some money so the people hosting it don't have to cover all the costs from their own pocket"...
Yes, and that's what led to most of them being sold pretty quickly as costs piled up. Internet Brands and VerticalScope were 2 of the major companies that bought out and consolidated a lot of them.
They're still around but the space has changed a lot and the forum software is outdated too. It's much cheaper to run servers now but most people have moved on to social or chat groups.
No, people who check in and post a couple times a day or so. The forums I loved (and some I still love, such as various fan forums the rollercoaster community runs), at least, weren't places where there was something new to consume every refresh where you'd sit on the site all day and refresh every 5 minutes - that... would've been extremely expensive on dial-up internet, for a start. You checked in with the community ever so often, and if there were people you got along with really well you'd add them on a messenger application! Unlike reddit, if you didn't get a response within 10 minutes, it didn't mean your post would sink into obscurity... probably everybody on the forum would at least see the title by the weekend.
You don't need to be paying for spam detection on a small community forum that is being actively moderated. Set up the software to prevent newbies from making new threads without moderator approval, use a DNSBL, have spam reports from anyone who's been around longer than a week automatically hide posts, remove said privilege from people who abuse it. I've never had a serious spam problem on a small forum I was actively moderating. Same with mailing lists. Also, if you do feel like you need spam detection, Akismet is available for free if your forum, like many, is non-commercial.