A fictional character's name, like a book or comic's title, and other short phrases, is not subject to copyright at all under US law, although in some cases it will be protected as a trademark. trademarks protect against use of a mark when selling a product or service, but do not prevent discussion of the trademarked item. Otherwise review sites could not legally exist.
An image of a fictional character, whether directly copied from an image created by someone else, or newly created in imitation of an existing image, is probably a copyright infringement. The newly created image would be a derivative work and so still subject to copyright protection. if the image is being used to identify the character as a subject of commentary, then it might be fair use, but that depends on the details of the situation.
It is not accurate that "revealing details about a fictional character on a for-profit website falls outside of fair use and makes the site owner vulnerable to a lawsuit." If details are revealed for purposes of commentary and criticism, that is very likely to fall under fair use, whether or not a profit is made. One could have a for-pay review site in which various fictional characters are described and reviewed, and the quality of their fictional presentation is discussed, and that would likely be fair use. Whether "details" are "revealed" is not the test for whether something falls under fair use or not. How much of the copyrighted work is used, whether the use harms the market for the original, whether the use is "transformative", and the nature and purpose of the use all matter.