The easiest way to pull data from another site is by using the Rest API. The interface is not as powerful as WP_Query in terms of the arguments you can pass to the query, but you can still do something like this:
$json = file_get_contents('http://example.com/wp/v2/wp-json/posts?tags=11&per_page=5');
$posts = json_decode($json);
The $posts variable now contains maximum five post objects with from tag with ID 11, which you can loop through in the normal way (assuming you are using WP 4.7 or higher).