Menu Entry with categories and items on one site

It will be good, when a meny entry has a site with list all entries and list all categories. And when click a category shows all subcategories and the entries.

And a filter for Alphabet will be good too! All alphabetic character and when click, show all entries with the choosen character in the current category.

Here is an example what i mean: http://www.yootheme.com/zoo/apps/index.php?option=com_zoo&view=frontpage&Itemid=5