I agree the fish in the photos is most likely Corydoras paleatus, commonly called the Pepper Cory. Asmodaues, you could "Google" photos of this species yourself and confirm the traits.
As for numbers, do not have less than five. You will have no issue with five in a basic 20g (which is 24 inches in length, whereas the 20g long is 30 inches length). Either will be fine with five or six of this species.
When considering stocking, one must never ignore the requirements of the species. Asmodaues, as you are asking the question I will explain this. Shoaling fish are fish that live in groups in their habitat. This is an important aspect of their requirements, and they will not be in the best of health unless they have several of their species with them. Different species have varying needs for shoaling, but in all cases one reason is security; they are programmed by nature to know that in groups they are safer. You cannot always see the effects of not providing this, and individual fish can vary somewhat, but generally speaking you cause stress to a shoaling fish if this critical aspect of its evolution is ignored.
The impact that a fish has on the biology of the aquarium can alter. Fish under stress impact the bioload more, because they are working harder and adding more to the water than fish that are not stressed. So when it comes down to it, having say one or two or three cories in a tank may well cause them stress which adds more to the bioload than if you had five or six. And when I say adding to the bioload, there is more to this than just the organic waste they produce. Allomones and pheromones are being released, and other fish read these, and this can in fact further increase the problems. It is like a domino effect.
So, your cories will be happier and therefore healthier with five or six in a 20g tank. Obviously, once can push this too far, but from what I've read and seen in this thread, we are not doing this. Providing sand will make a big difference too, as cories need to sift the sand through their gills, something they cannot do with gravel. And being regular with weekly water changes of half the tank will help as well.
Byron.