What can be done to reduce the lines and the pouchy sags just to the outside and below my mouth corners? (Photos)

Combination treatment will work best. I would start by addressing facial volume loss using a collagen stimulating filler like Sculptra Aesthetic. I would follow this up by placing the newer flexible gel hyaluronic acid based filler, Restylane Refyne, into the lines themselves. Finally, I would consider skincare and possible skin resurfacing treatments to improve the quality of the skin itself. 

This area of concern will require a multi-faceted approach.  Most often I will address this area using fillers to support, add volume, and fill the fine lines.  Sometimes I would add novathreads, both smooth and barbed,  to lift and stimulate the area.  This might be combined with micro-needling, peels, and laser treatments to further help the skins surface.  A consultation with a provider that offers a combination of the above services would be best.