First, I would like to get a list of recent posts to display on the sidebar. What template tag can I use for this?
Second, I would like to get a list of certain categories to display. I know how to get a list of all categories, but I want to segregate the categories. Is it possible to have categories of categories?
1. Your questions have nothing to do with “lists” (as stated in the title)
2. The easiest way – get a recent_posts plugin. SEarch the Codex.
3. Again the Codex. See the http://codex.wordpress.org/Template_Tags#Category_tags – some of them let you display categories one by one
4. Catgeories of categories? Do you mean subcategories? Yes. See your admin panel.