How to have new activity count above any view? I have seen on your website, when there is a new question posted, the list shows a new activity button with a count above the list. How can I do that in Drupal with any view?

I am interested in showing such a thing with Statuses. There is an option in statuses settings to show a refresh button below the status stream when there is a new activity, but I want to show it above like on stackexchange and with a count.
Have a look at the Menu Badges module to add such notifications to any menu item and/or menu tab of your choice.
Here are some details about it (from its project page):

Provides a method for adding iOS-style badges to menu items. (see screenshot)

Adding Badges to Menus
Once enabled, go to Administration &gt; Structure &gt; Menus, and click &quot;list links&quot; next to the menu containing the target item. Click &quot;edit&quot; next to the item and select the badge to display with the Display Menu Badge select box.
Adding Badges to Tabs
For adding badges to menu tabs, there is a tab under Administration &gt; Structure &gt; Menus called &quot;Tab Menu Badges&quot;. Search for the menu router path of the tab you want to alter, then select a badge from the corresponding select box.
Badge Types
The module includes five example badges, and new badges can be created easily with Views. Modules can also supply their own badges with a hook implementation. See the README.txt file for details.

Because of how it integrates with the Views module, you basically reduce the solution for any type of notification to something like &quot;Just create an appropriate view of it&quot;.
Video tutorials:

Defining Menu Badges with Views in Drupal, from the module maintainer, which shows how to use it for a custom view with a menu tab &quot;unpublished content&quot; within admin/content.
Drupal 7 Menu Badges Module.