Categories and Tags cannot be assigned to Pages. Pages are for static content that rarely, if ever, changes. Categories and Tags can only be assigned to Posts.
When we publish a post (not a page) with Categories and or Tags assigned to that post (not page) the software automatically displays it on the Categories and Tags pages we assigned to the post, as well as on Archives pages. This is not a page we bloggers create at all. It's created by the software.
A custom menu allows you to display Categories with drop-downs to sub-categories in tabs along the horizontal navigation where normally only Pages tabs are displayed. If you wish you can also include Pages with drop-downs to sub-pages and/or Tags pages and/or Custom Links in your custom menu as well. You are in charge of what appears in a custom menu. You choose the order in which to display any and/or all the foregoing in your custom menu. You choose which to display and which to hide.
Here’s a link to a custom menu walkthrough > http://onecoolsitebloggingtips.com/2011/08/11/wordpress-com-custom-menu-walk-through/
There are many common errors, misunderstanding and misconceptions when creating custom menus and you can read about them here > http://wpbtips.wordpress.com/2011/12/19/custom-menus/