I want to upload an app to various app stores, and profit from it. Do I have to be registered as a "moral person" or can I get profit of it as a "natural person"? Also I want to know if I have to pay taxes on the income from the app (I'm from México).
I think you are being confused by the terms "moral person" and "natural person". They actually mean the same thing, which is distinct from "legal person".
A "moral person"/"natural person" is what us non-lawyers would call "a person". A "legal person" is an entity that has legal rights and obligations. For example, they are entitled to due process, and are obligated to pay takes and obey laws. All "natural persons" are "legal persons," however, NOT all "legal persons" are "natural persons". Examples of legal persons who are not natural persons include most companies and non-profit organizations.
This means that a corporation can make contracts, sue people, and be guilty of a crime (rights/obligations given to all persons), but (in the USA) cannot vote (which is restricted to, among other restrictions, natural persons).
In answer to your actual question:
I am not a lawyer. I am not your lawyer. This is not legal advice, nor a substitute for legal advice
You are probably okay. I know multiple people who have sold apps in an online store, without using a corporation to do so. However, note that you a) will probably want to check this with a lawyer, b) will probably need to pay US taxes on your US income, c) will definitely need to declare/pay Mexico taxes on your income from this.