Hi,
1. The module "Associated products listing for category listing menu 576" is used by the menu with the id 576. You can find the menu via the menu Display->Content menus. There, once you open its options, you will see that "Associated products listing for category listing menu 576" module in the "associated modules" option of the menu.
One menu can display several categories and thus you can have one module to display several products listings...or not. It really depends on how your configure your menus and modules.
2. In understood what you were talking about. And so my answer is the same. The simplest to do is this:
edit each menu and module you created via the menus Display>Content menus/modulesand change their options to what you want. If they all have the same options, it will display the same.
I can give you an example if you want...
Take the "photographic print" menu at the top:
66.147.244.189/~treegirl/index.php/shoppe/photograhpic-prints-2
Its id is 589. You can edit it via the menu Display>Content menus.
It's a menu of the type hikashop category listing, so it's displaying the child categories of the category you have configured in the "associated category" option of the menu.
As you can see you don't see any category listing for that menu. That's because the "associated category" you selected doesn't have any child categories.
Also, there is the module with the id 135 which is set in the "associated modules" option of that menu. That's this module which displays the child products of the "associated category" you selected in the menu.
So if you change the options of the menu, it will change the display of the categories (but there are no categories there), and if you change the options of that module, it will change the display of the products listing.
What I can see based on your screenshot, is that you simply would like to have the description of the category displayed for that menu. It's quite simple. In the options of that menu, just turn on the "show description" option and that's all.