Regarding "Thou shalt not kill"

I am still in the story of Yitro and the Ten Commandments. I have a few questions if you allow me:
"Thou shalt not murder" is a universal and binding categorical commandment in every situation, and is imposed on every person regardless of their halakhic commitment. The fact that "Thou shalt not murder" appears as a halakhic commandment (one of the Ten Commandments) means that it comes to promote religious values. What is that halakhic dimension (which concerns Jews only) that is not included in the categorical commandment?
In the context of halachic statements, you distinguish between a normative statement that cannot be changed and a factual statement whose validity can change if the situation changes. In light of this, "You shall not murder" is a normative halachic. Is it possible to say that the halachic "whoever comes to kill you, hurry to kill him" is a factual statement and not a normative one? I want to be precise about the fact that the statement is "whoever comes to kill you" and not "whoever comes to kill you, hurry to kill him" because "You shall not murder" is a categorical command and therefore is also normative. Does that seem right to you?
And finally, what is the legal status of blood atonement or blood revenge, since from the perspective of the categorical imperative they are murder?