Board Thread:Support Requests - Community Management/@comment-26362571-20150818221506/@comment-4731443-20150818231805

Help:Category should answer all your questions regarding categories. You should be able to remove a page from a category by clicking the garbage bin icon next to the category name either at the bottom of the article in view mode, or in the right panel in edit mode. Note however that some templates add categories to pages they are used on (like Stub), in which case I don't think you can remove the article from that category without modifying the template (or removing it from the article).

If by tabs you mean the navigation bar at the top of your wiki, you need to go to MediaWiki:Wiki-navigation on your wiki. There you can add first-level items with one asterisk, and second-level items underneath them with two asterisks. You'll notice that those links don't need brackets like articles do. Example: *Suggested reading This will show a Suggested reading tab with a link to the Science category underneath, displaying as Science!, followed by a Nothing tab without any links in it.
 * Category:Science|Science!
 * Nothing