Hi,
You can ue that coed in the "product / show_default" view to have all the categories informations:
$productClass = hikashop_get('class.product');
$categoryIds = $productClass->getCategories($this->element->product_id);
$db = JFactory::getDBO();
$categories = array();
foreach($categoryIds as $k => $category){
$categories[$category] = new stdClass();
$db->setQuery('SELECT * FROM '.hikashop_table('category').' WHERE `category_id` = '.$category);
$categories[$category] = $db->loadObject();
$db->setQuery('SELECT * FROM '.hikashop_table('file').' WHERE `file_ref_id` = '.$category);
$categories[$category]->image = $db->loadObject();
}
All is in the var $categories.
Regarding the url to each category, there is no default url, you have to create a menu listing the categories.
Then create dynamically the urls depending on the previously created menu.