Hello!
We don't do a regularly-scheduled newsletter, but we do send a email update about once a month with upcoming opportunities and important news. We try to limit communications to when it is really needed so people are more likely to read them. Padded newsletters can be easy to ignore. We post more general updates on our volunteer website, so people can check it out if they feel like it, but it isn't sent to their inbox.
We don't have a closed Facebook group at my current organization, but we had one at my previous organization. It was a great way to build community, and we could also use it to send out recruitments, reminders, updates, and fun stuff. The amount of time it takes to moderate depends on the number of volunteers who actively use it. Maybe you could consider a volunteer moderator?
We have a suggestion box, and we also send out periodic evaluations so volunteers can provide feedback. I've found that people rarely use the suggestion box, but the evaluations can be very helpful.
:)