Reviewing through your inquiries only edits on documents should produce a notification to users. However if you are interested in seeing this type of feature I would suggest submitting an idea to the Ideas for Jive space where our product managers review through top rated ideas when considering features for future releases.
Also, is there a way authors can receive notifications of their own postings?
If they are following the blog where the blogposts are located I would expect them to receive a notification. Additionally, if a user follows their user they would also receive updates on content they create.
I found a workaround if you deliberately would like to send notifications on blog updates- Use the "Schedule when to publish" feature and set it for ~1 minute after the current time. This will re-send notifications.