In Drupal 7, what is the proper syntax to call the theme function for a node, passing an argument?
The function you're looking for is node_view():

$view_mode = 'teaser'; // Or 'full'
print render(node_view($node, $view_mode));


It's the same function that Drupal internally calls to display the node page/teaser so your template files will be honoured as you'd expect.