Cookies – I use 1/2 cup shortening and 1/2 cup butter in baking chocolate chips cookies but they always fall flat

My guess:

With a little oven you probably don't preheat as long, and when you open the door you let ALL the hot air out. You need to reheat the air in the oven after the cookies go in for them to cook. Because the hot walls and rack are much smaller (and probably not as well heated to start with), it's harder for them to reheat the inside of the oven.

So the temperature is lower when you start the cookies. Some (maybe a lot) of the cooking time is spent getting the oven, the baking sheet and the air back up to temperature. Cooking them longer or at a slightly hotter temperature should help with this.

Welcome to Seasoned Advice first I will point you to an article in our blog Silpat, Parchment Paper or Plain Baking Sheet. @KatieK contrasts these cooking surfaces.Look at the instructions for time and temp. Are you thoroughly Preheating? You pictures indicate that you are using parchment, but you don't mention time/temp.

My first inclination based on what I see is that you are baking them too long at too low a temp, and not fully preheating. If you raise the temp and shorten the time the cookie will not spread as far. With 'scoop' cookies you expect the dough to spread some, but you are getting too much spread. The higher temperature will cause the cookie to form a solid (ok, solidish, it should be soft but 'strong enough' to hold form) This will also give you better "bottoms" as they will bake faster as well.

Another thing you might be doing is opening the oven door too often, this releases a lot more heat than you think, extending the correct baking time and slowing the process. I know it is sometimes hard to resist peeking, try to not open the door till you are at least 75% through the projected time.