load node_type_form form I need to load and print drupal 'internal' form on the page, which id is "node_type_form"
I have:

$form = drupal_get_form("node_type_form");

$html = drupal_render($form);

echo $html;

it only prints "Menu settings" and "Save and add fields" button.

I get:

Notice: Undefined index: node_type_form in drupal_retrieve_form()

Warning: call_user_func_array() expects parameter 1 to be a valid callback, function 'node_type_form' not found or invalid function name in drupal_retrieve_form()

Notice: Trying to get property of non-object in menu_form_node_type_form_alter()
Notice: Undefined index: #node_type in menu_form_node_type_form_alter()
node_type_form() lives in modules/node/content_types.inc, which the system only includes when it needs to (to fulfil menu paths etc).

If you include it manually before your call to drupal_get_form() it should work...

module_load_include('inc', 'node', 'content_types');
$form = drupal_get_form("node_type_form");
// ...