Is it possible to render a twig template for "later use"?
Normally you don't render twig templates directly, but build the content in a render array and use the render service:

public function nodeExportPdf(NodeInterface $node) {
  $view_builder = \Drupal::entityTypeManager()-&gt;getViewBuilder('node');
  $build = $view_builder-&gt;view($node, 'full');
  $html = \Drupal::service('renderer')-&gt;renderPlain($build);
  ...
}


This will use the node template configured for the view mode you specify in the view builder. In this example full, but probably you want to create a custom view mode for the pdf.

When you are in a controller you get the route parameters in the function arguments. How to build the route for this see https://www.drupal.org/docs/8/api/routing-system/using-parameters-in-routes