Export Magento categories with ID using php script

Copy the code below into a new file "categorywithid.php" and place this file in your root folder

define('MAGENTO', realpath(dirname(__FILE__)));
require_once MAGENTO . '/app/Mage.php';
Mage::app();

$category = Mage::getModel ( 'catalog/category' );
$tree = $category->getTreeModel ();
$tree->load ();

$ids = $tree->getCollection ()->getAllIds ();

if ($ids) {
 $file = "var/export/catwithid.csv";
 file_put_contents($file,"catId, catName\n");
 foreach ( $ids as $id ) {
   $string = $id . ', ' .$category->load($id)->getName() . "\n";
  file_put_contents($file,$string,FILE_APPEND);
 }
}

Hit Your browser like www.YourDomain.com/categorywithid.php Thats it. You are done. Get the csv file under "var/export/catwithid.csv".

How to get Parent category id in Magento?

Here is the code to get parent category id.
$current_category = Mage::registry('current_category');
echo $parent_id = $current_category->parent_id; 

Magento how to get category id in product page?

<?php $categories = $_product->getCategoryIds(); ?>
<?php foreach($categories as $k => $_category_id): ?>
    <?php $_category = Mage::getModel('catalog/category')->load($_category_id) ?>
    <a href="<?php echo $_category->getUrl() ?>"><?php echo $_category->getName() ?></a>
<?php endforeach; ?> 

This will load and link all of the categories that the product is found in.