I think that the themes you identified are essential to understanding the overall purpose of the play. Early on in the drama, the murder of Hamlet's father is cast as an act of disorder. The terms of "rotten" as well as the slaying of Caesar help to bring to light that the act committed has brought about a sense of disruption to the natural order of old Hamlet's rule. I would suggest spending some time in analyzing these terms in the first act. Part of the root of Hamlet's misery is that the death of his father was unnatural, and disrupted the hope of moral order. His agony is rooted from this inability to bridge the gap between the moral order which should be and the disorder that is. Continuing this would be how each character dies an unnatural death, contributing to the overall feel of disorder which is present in the actions of individuals in the play.