The difference between manners and morals is that the former are necessarily social in nature whereas the latter are not necessarily social in nature. So the rules of etiquette do not apply when one is alone.
Manners = necessarily social
Morals = not necessarily social
Rules of etiquette = don't apply when one is alone AKA rules are etiquette are about manners (morality - maybe?)
A. One could be immoral without ever having caused any other person any harm. -- Correct. Since morals are not necessarily social therefore, one can be immoral in private while being mannered in socials.
B. No immoral act could be a violation of the rules of etiquette. -- Not all moral acts are "not social". Some may be social, some not. Those immoral acts which are social could violate the rules of etiquette. Incorrect.
C. The rules of morality apply only when one is alone. -- "only" is incorrect. The stem says "not necessarily". Sufficient but not necessary condition. Incorrect.
D. It is more important to be moral than to have good manners. -- Completely irrelevant. Eliminate.
E. What is social in nature could not be a matter of morality. -- Similar to B. Morality can be social or private (not social). Eliminate.