Hi,
1. On some of your products listings, you configured the products listing with the text centering turned off and/or a big margin. Changing these options in your menus/modules options via the menus Display->Content menus/modules would solve that.
On the page you gave a link to, all the text below the image/add to cart area is the product description. He just has a well structured product description HTML. You can also put images in the product description. So it's quite easy to do.
2. To display the product code on the products listings, you will have to edit the file "listing_img_title" of the view "product" for your front end template via the menu Display->Views and add the code:
echo '<br/>'.$this->row->product_code;
after the code:
echo $this->row->product_name;