BuddyPress.org

With a little looking around I think I’ve answered my own questions, but I’ll reply to myself in case it helps others:

– yes, you can have private groups that have private conversations

– I’m not sure if the admin can sign up individuals from the admin and start private conversations from the admin, but I’m thinking if the admin had an account they could start groups and discussions like a regular user, and being a member of those areas can be an advantage.