Form is not being rendered in template file
Drupal render will return the html

drupal_render(drupal_get_form('form_id'));    


you have to print the returned html as well.

print drupal_render(drupal_get_form('form_id'));


in your case 

$form_template = drupal_get_form('questionnaire_template_form' , $variables['entity']); 
drupal_render($form_template);


change it to

$form_template = drupal_get_form('questionnaire_template_form' , $variables['entity']); 
print drupal_render($form_template);