1,2,3,5 are different descriptions and degrees of murder. In so much as we people share the same nature as those murdered in those examples, it is unnatural (insane) to murder one’s own nature. So they are clearly evil.

4 is justice and does not fit in my understanding.

One reason, and it is only one of many, is that capital punishment brings the imminent threat of certain death to the forefront of the killer. It imposes the reality of the evil he has done onto his consciousness in a way nothing else - perhaps most especially lifetime incarceration*- can.

This can bring him to the point of repentance and, having destroyed one life and ruined his own in the process, offer the most realistic chance to proximate repentance and salvation of his soul.

Since we people all share the same nature then it would seem to me to be sane to support capital punishment as salvation is a (the only) rational goal.

There is a very rational caveat to say that the certainty of conviction of capital crimes (man is fallible) means that the chance of an innocent on death row is too big a risk thus capital punishment is too unsafe to support. I think this is a reasonable argument to try to make.