How do I use hook_theme() in a module?
The proper way to assign a theme function to a form using hook_form_alter() is like this:

function footer_menu_form_footer_menu_node_form_alter(&amp;$form,&amp;$form_state,$form_id){
  $form['#theme'] = 'pz_footer_menu_node_form';
}


I can't tell if you're using Drupal 6 or 7; you're using the arguments property in your theme declaration which is only valid in Drupal 6, and also the render element property which is only valid in Drupal 7. 

Judging by the out of memory error I'm guessing Drupal 7. As you call drupal_render() on the the $form object in your template file, it runs that variable back through the same theme function, and you end up with an infinite loop.

Try changing the last line in your template file to this:

&lt;?php print drupal_render_children($form); ?&gt;


That should stop the error from happening.