The way to create drop-downs from Pages to sub-pages and/or from Categories to sub-categories is to create a custom menu. To do that you need to have a clear comprehension of the differences between static pages and posts and between static pages and dynamic pages in a blog.
Staff have provided help for those who want to structure their blog like a website. > http://en.support.wordpress.com/using-wordpress-to-create-a-website/
What’s critical is:
(1) a clear comprehension of the differences between pages and posts > http://en.support.wordpress.com/post-vs-page/
(2) a clear comprehension of the fact that there is only one dynamic page in a blog for posts and we cannot post to more than that one page, but we can create the appearance that we have posted to more than one page.
We organize our posts by assigning Categories to them. When we publish a post it automatically appears on the dynamic running page for posts and also on the dynamic Categories pages, dynamic Tags pages and dynamic Archives pages. Note: There must be one published post in each Category/Tag in order for there to be anything to display.
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 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. http://en.support.wordpress.com/menus