Hi,
1. For the height of the category boxes, that's because one of the categories on your listing must have a lot of sub categories. In the settings of your menu item, under the categories options tab, I would recommend to turn off the display of the sub categories.
That will avoid all that empty space.
2. Regarding the categories listings missing the product listing, if you have the file templates/YOUR_TEMPLATE/html/com_hikashop/category/listing.php rename that file and it should then work properly.
3. Regarding the category description at the top, make sure that you have the "show description" setting activated in the settings of your menu item via the Joomla menu manager.