How can I display latest post in another menu tab?
You could use taxonomies.  First, navigate to admin/structure/taxonomy and create a taxonomy with the terms you want to have tabs for (e.g. QUESTIONS, TAGS, USERS, BADGES, UNANSWERED).  Hover over each of the terms in the list terms to discover their default paths.  Let's say you note that "BADGES" has been assigned the path "taxonomy/term/7"

Now, all you need to do is to create an item in your main menu to display tagged articles. So navigate to admin/structure/menus and add the following link to the main menu. Set Menu link title to "BADGES", and Path to "taxonomy/term/7".  Repeat for other taxonomy terms you want to access via a main menu tab.

Now, you have tabs in your main menu called "BADGES", etc.  Under each tab content tagged with its taxonomy term will appear automatically, so to make content show up under the BADGES tab, tag it with "BADGES".  If you're using Drupal 7, the default article content type already has a taxonomy field.  But you can add a taxonomy field to any content type if it is missing.

You can now refine this by customizing how things are listed using Views to create customized listings. You can also hide the numeric paths with the use of URL aliases if you want (so the path appear to the user as badges instead of taxonomy/term/7.)