How can you query for nodes, terms etc of a drupal 7 website from your drupal 8 website? 

You can add external databases in your settings.php file:

$databases['external']['default']= array(
  'database'=>'',
  'username'=>'',
  'password'=>'',
  'prefix'=>'',
  'host'=>'',
  'port'=>'3306',
  'namespace'=>'Drupal\\Core\\Database\\Driver\\mysql',
  'driver'=>'mysql',
);

Then, in a custom module you can query for nodes, terms etc.

// Switch to external database
\Drupal\Core\Database\Database::setActiveConnection('external');

// Get a connection going
$db = \Drupal\Core\Database\Database::getConnection();

$vid = 5; // The vocabulary I want to query
$query = $db->select('taxonomy_term_data', 't');
$query
  ->join('taxonomy_term_hierarchy', 'h', 'h.tid = t.tid');
$query
  ->addTag('translatable')
  ->addTag('taxonomy_term_access')
  ->fields('t')
  ->fields('h', array(
    'parent',
  ))
  ->condition('t.vid', $vid)
  ->orderBy('t.weight')
  ->orderBy('t.name');
$results = $query->execute()->fetchAll();

Switch back to your current db

\Drupal\Core\Database\Database::setActiveConnection();

Save the results to a d8 vocabulary

foreach($results as $result) {
  Term::create([
    'tid' => $result->tid,
    'name' => $result->name,
    'vid' => 'my_d8_vocabulary_name'
   ])->enforceIsNew()->save();
}