Hello theant,
Unfortunately my Italian is really really bad. From what I can make of it, you haven't assigned all your subcategories to menu items.
If you want your search results to be posted on a specific page you need to do some coding.
First assign a menu item to your search results and write down its ID. Then override the K2 Tools module and more specifically the search.php file
And then make the following changes,
<form action="<?php echo $action; ?>"
should change to
<form action="<?php echo JRoute::_('index.php?option=com_k2&view=itemlist&task=search&Itemid=YOUR_MENU_ITEM_ID'); ?>"
Finally assign the modules you want that menu item