Magento – how do get all parent of curent category in magento2

$category->getPath() will return the ids of all categories from the tree root to the current one separated by slash (/). Here is an example: 1/2/56/124/543. The first one is the 'root of roots'. The second one is the catalog root (default category). The rest of them are simple categories. So you can do something like this.

$path = $category->getPath();
$ids = explode('/', $path);
if (isset($ids[2])){
    $topParent = Mage::getModel('catalog/category')->setStoreId(Mage::app()->getStore()->getId())->load($ids[2]);
}
else{
    $topParent = null;//it means you are in one catalog root.
}

Now you can get the name and url like this:

if ($topParent){
    $name = $topParent->getName();
    $url = $topParent->getUrl();
}

You can load the attributes collection and get it's first element:

$categories = Mage::getResourceModel('catalog/category_collection');
$categories->addAttributeToSelect('*');

$categories->addAttributeToFilter('url_key', 'cat_urlkey');
$categories->addAttributeToFilter('path', array('like' => '1/15/%');

The second condition tells to take subcategories of the category with id 15.