Well actually, the article defines it as "the logic of action," but it is commonly understood/applied to the action of human beings (see the definition given
here).
As far as psychology goes, they are very different doctrines - psychology would attempt to find the causes of human action; praxeology looks at the logistics of it. Psychology might be able to determine why a human acts in a certain way, but praxeology establishes the univeral rules which humans must act under.
To me, these axioms are true due to the logical consequences of the very definitions of the words involved. That both parties must benefit from a voluntary exchange is axiomatic, because no one would engage in such an exchange without benefitting (albeit this is a simplified version - one must discount fraud and put "benefit" in a certain context).