Filter/sort content displays/listings
Views allows you to expose sorts, but doesn't create the type of UI you are asking for by default.

What you get by default with views after clicking 'expose' at the top of your sort value is two menus, one for the value to sort by, and one for the sort direction.

The most important thing to remember here is what you get in your view's url after submitting this original exposed filter form: /myviewpath?sort_by=XXXXX&amp;sort_order=XXXXX.

You can write your own custom module, do a hook_form_alter of the existing form, a fancy jquery widget, heck write it in Flash if you really want to, all the view cares about is you passing those two values and that those values are enabled and available for that view. 

In terms of getting your own custom values available there have a look at the views sort class documentation and the view_handler_sort_* examples already provided in /views/handlers. Views argsort looks pretty interesting as well if you don't want to write your own sort handler but haven't tried that module myself yet.

For part 2 of your question this summary is already provided by views. Click on header, click on "Global Result Summary", and use the tokens provided to create your summary.