A Facebook user posts a series of comments in a public Facebook forum. Can I use those postings in an article to be published in a newsletter?

As a general matter, any work of authorship -- including this response to your question -- created in the United States is copyrighted immediately upon its creation. The author of the work has the right to determine whether and to what extent others may copy, publish and reproduce the work. There are exceptions to this rule, including the rule of "fair use"; whether your proposed newletter use qualifies as "fair" is impossible to determine from the facts you have posted. As a general matter, you do not have the right to reproduce the works of authorship of others.