Existentialism is the idea that our existence is the only life we have, not a pre-destined soul that will go to heaven or hell. Throughout the series, The Elric Brothers bear this existentialist view of the world (and Edward flat out says he's an atheist, or secular, depending on the translation). They don't believe in heaven or hell, and yet they struggle with the idea of harming other's. They repeatedly state that they would prefer to avoid killing or harming other's in their quest to finding the philosopher's stone. To some, this may be paradoxical, or contradictory to their existential beliefs. If there is no afterlife, then why worry about harming others? Well, I posit that the Elric Brother's would subscribe to the idea of positive and negative rights. Here's an excerpt from the wikipedia article on the subject:
Under the theory of positive and negative rights, a negative right is a right not to be subjected to an action of another person or group—a government, for example—usually in the form of abuse or coercion. As such, negative rights exist unless someone acts to negate them. A positive right is a right to be subjected to an action of another person or group. In other words, for a positive right to be exercised, someone else's actions must be added to the equation. In theory, a negative right forbids others from acting against the right holder, while a positive right obligates others to act with respect to the right holder.
The Elric Brother's subscribe to this idea that one should do what they want without harming other's, which is exactly the role that the Ubermensch plays. He lives according to his own rules, but he doesn't impede the right's of others in the process.
Alchemists can not create, they can simply transform. This is why Edward can create swords from pools of blood and things of that sort. If he repairs Alphonse's armor, the metal becomes thinner because he must use that very same armor to repair it. When the Elric Brother's go to Youswell, Edward trades the deed for the town from the military guy who ran the town for practically nothing. Edward informs the townspeople that he was going to extract a heavy fee for their freedom, and his price was a night's room at their local inn. So what does this mean? Edward Elric, and all alchemists in general, exemplify this idea of equivalent exchange in everything they do, even outside of alchemy. Albeit, the idea that a night at an inn is an equivalent exchange for the deed of the town is an absurd one, but it's a personal philosophy that Elric adhered to, nonetheless. This idea of equivalent exchange could be applied to practically anything. For every action, there is an equal and opposite reaction. The idea of "Karma" supports this. To get better grades, one must sacrifice a few hours to study. For muscles, one must exercise. If you want a bag of Doritos™ and a Blu-Ray copy of Batman™ Vs Superman™: Dawn of Justice®, one must pay a cheap fee of 19.99.