//Instantiate an token object.
$token_service = \Drupal::token() ;
// Pass the string which contains the token and context(Eg: node object, user object et..)
$token_replaced = $token_service->replace($string,['node' => $node_object ]);

//Your custom URL (alias).
$my_url_alias = 'about-me';
// This line will return corresponding system path.
// Lets say, '/node/15' is correcsponding path '/about-me'
$path = \Drupal::service('path.alias_manager')->getPathByAlias('/'.$ahurl);
if(preg_match('/node\/(\d+)/', $path, $matches)) {
// This will load the node object.
$node = \Drupal\node\Entity\Node::load($matches[1]);
}

// Get the block machine name from the block configure option of the desired block.
// And you'll get url like this /admin/structure/block/manage/bartik_search. 
// The last part of the parameter is the block id
$block = \Drupal\block\Entity\Block::load('bartik_search');
$block_content = \Drupal::entityManager()
  ->getViewBuilder('block')
  ->view($block);
 
return array('#markup' => drupal_render($block_content));