Can I use GitBook to publish an F.A.Q. like this one?

You can create an F.A.Q. with GitBook. As a matter of fact, this Help Center is made with GitBook and hosted on GitBook.com.

To create an F.A.Q., you can install and use the theme-faq. Soon, you will be able to choose a F.A.Q. template from the book creation page on GitBook.com.