And the vulnerable are sitting ducks for opportunists. They can be made dead against their will simply because they are unable to communicate. Or, if they can communicate, it is covered up so they can be murdered.
Very often true, but those are not necessary limits on the definition of murder. Murder means to do what only God has a right to do: to end somebody's life.
Your proposed definition is inadequate because it does not take account of murders in which the murderer may have perverted noble intentions and no personal gain in mind: e.g. the killing of a handicapped baby, slaughtering someone as a sacrifice because of the belief that Huitzilopochtli or some other a god or gods required it, etc.
In the case of a Just War or the death penalty, the state is specifically authorized to act in God's name by God's word:
Romans 13:4
For [the ruler] is God's servant to do you good. But if you do wrong, be afraid, for he does not bear the sword for nothing. He is God's servant, an agent of wrath to bring punishment on the wrongdoer.