Close except that the formation of DNA, cellular systems, or even orbital mechanics and quantum events are not "random."
They follow very detailed, exact laws of the chemical and physical interactions that determine chemical reactions, protein structures, and physical events.
Simple example: salt is not formed and its structure determined by sodium and chloride atoms just randomly bumping into each other and sticking together in a random fashion. The many laws that describe ion dissociation, electron valencies, bond mechanics, etc. determine that one sodium and one chloride bond at a specific angle.
While you've pointed out some circumstances that must exist to permit the occurance of certain constructs, I don't believe you have made clear that the existence of those circumstances did not occur through random and unplanned events.