Magento 2 – Understanding Web API Integration

It seams that the API for categories does not work similar to the products. For the products you can get and set 'additional_attributes'.
In my opinion you need to extend the type definitions for the category methods to make your field behave just like the core fields.
Here are some details about how you can extend the type definitions The explanations are for extending types related to the products, but you can do the same for categories.
The main idea is to create an extension, add the file etc/wsdl.xml inside the extension (and wsi.xml if you use WSI Complience). In wsdl.xml add your missing attributes, and Magento will merge your file with the ones from the core.
You need to extend the following types catalogCategoryInfo, catalogCategoryEntityCreate

As i understand your query, here is the method to get the api data, into xml format first.

$xml contain xml response you have made to get the data from api.

$soap_do = curl_init();
            curl_setopt($soap_do, CURLOPT_URL,            $url );
            curl_setopt($soap_do, CURLOPT_RETURNTRANSFER, true );
            curl_setopt($soap_do, CURLOPT_SSL_VERIFYPEER, false);
            curl_setopt($soap_do, CURLOPT_SSL_VERIFYHOST, false);
            curl_setopt($soap_do, CURLOPT_POST,           true );
            curl_setopt($soap_do, CURLOPT_HTTPHEADER, $headers);
            curl_setopt($soap_do, CURLOPT_POSTFIELDS,    $xml);

            $result = curl_exec($soap_do);

            curl_close($soap_do);
            //echo $result;
            //echo $result_array = json_encode($result);
            //echo   $description = $result->extendeddescription;

$p = xml_parser_create();
xml_parse_into_struct($p, $result, $vals, $index);
xml_parser_free($p);

After you can break the xml into array and get the value. here $vals contains the valid array of xml comes data. If you want to import the product as find into xml array you need to run new product making script with valid input param comes form api.

The Below code, you can used to add or update new category

$category = Mage::getModel('catalog/category');
                                                  $category->setStoreId(0); 
                                                  $categoryName = $cate;
                                                  $rootCategory['name'] = $categoryName;
                                                  $rootCategory['path'] = "1/2"; 
                                                  //$rootCategory['display_mode'] = "PRODUCTS";
                                                  $rootCategory['is_active'] = 1;

                                                  $category->addData($rootCategory);
                                                  try 
                                                  {
                                                    $category->save();
                                                    $CategoryId = $category->getId();
                                                  }
                                                  catch (Exception $e)
                                                  {
                                                    echo "categories not found";
                                                  }  

And for product adding you need to follow the below script with valid input params

$obj = Mage::getModel('catalog/product');
$_product = $obj->load($productid); // Enter your Product Id in $product_id
// get Product's name
$name = $_product->getName();
//get product's short description
$shortdes = $_product->getShortDescription();
//get Product's Long Description
$des = $_product->getDescription();
//get Product's Regular Price
//echo $_product->getPrice();
//get Product's Special price
//echo $_product->getSpecialPrice();
//get Product's Url
//echo $_product->getProductUrl();
//get Product's image Url
//echo $_product->getImageUrl();
//echo "<pre>";print_r($_GET);exit;

/*********Getting values*********/

$optionval1 = $_GET['optionval1'];
$optionval2 = $_GET['optionval2'];
$optionval3 = $_GET['optionval3'];
$optionval4 = $_GET['optionval4'];
$image = $_GET['image'];
//print_r($image);
$image_parts = explode('/',$image);
$count = count($image_parts);
$final_image = $image_parts[$count-1];
//echo "<pre>";print_r($image_parts[$count-1]);exit;
$price = $_GET['price'];
$product = Mage::getModel('catalog/product');
$product_sku = time();
$product->setSku($product_sku);
$product->setName($name);
$product->setDescription($des);
$product->setShortDescription($shortdes);
//-- price section
$product->setPrice($price);
//$product->setSpecialPrice(10);

//----- company address and map
$product->setTypeId('simple');
$product->setAttributeSetId(9); // default
$product->setCategoryIds(array(20)); // need to look these up

$product->setWeight(1.0);
$product->setTaxClassId(2); // taxable goods
$product->setVisibility(3); // search
$product->setStatus(1); // enabled
$productQty = '1';

//$stockData=$product->getStockData();
$stockData['qty']=$productQty;
$stockData['is_in_stock']=1;
$stockData['manage_stock']=1;
$stockData['use_config_manage_stock']=0;
$product->setStockData($stockData);

// adding images to product
$abspath = getcwd();

$path = "./final_images/new/".$final_image;
//print_r($path);
?>

<?php 
if (file_exists($path)) {
    $product->addImageToMediaGallery($path,array('image','small_image','thumbnail'),false,false);
}

$product->setWebsiteIds(array(Mage::app()->getStore(true)->getWebsite()->getId()));
$product->save();
/*********** custom option for cart ***********/
  $new_product_id=$product->getId();
                                        $product = Mage::getModel('catalog/product')->load($new_product_id);
                                        $optionData = array(
                                                'is_require'        => false,
                                                'title'             => 'Select Font',
                                                'type'              => 'drop_down',
                                                'sort_order'        => 0,
                                                'values'            => array(
                                                    array(
                                                        'is_delete'     => 0,
                                                        'title'         => '12',
                                                        'price_type'    => 'fixed',
                                                        'price'         => '',
                                                        'sku'           => '',
                                                        'sort_order'        => 0,
                                                    ),
                                                    array(
                                                        'title'         => '18',
                                                        'price_type'    => 'fixed',
                                                        'price'         => '',
                                                        'sku'           => '',
                                                        'sort_order'        => 1,
                                                )),
                                            );
                                        $product->setHasOptions(1);
                                        $option = Mage::getModel('catalog/product_option')
                                                  ->setProductId($new_product_id)
                                                  ->setStoreId(1)
                                                  ->addData($optionData);
                                        $option->save();
                                        $product->addOption($option);
                                        Mage::app()->setCurrentStore(Mage_Core_Model_App::ADMIN_STORE_ID);
                                        $product->save();
/*********** custom option for cart end***********/
$productid = $product->getId();
$result['product'] = $productid;
echo $result['product'];

Hope this will help you, or make sense what you should need to do.