Hi,
The title of the module is displayed by your template if the "show title" option of your module is turned on and that the style of the position where you put your module handle the module title display (that's something to see with your template provider).
The products listings modules and menus all use the same views. So when you override the products listing view file, it will be for all of them. So you would have to add a check on your changes so that they apply only if you are displaying the listing in that particular module:
if($this->params->get('id')==XXX){
//custom code for the module with the id XXX
}