why should any part of the government be empowered to take away an American’s ultimate right to live?

In most cases, it is an individual defending himself. Not so much the state deciding life or death.

A police officer has just as much right to defend themselves from harm as anyone else. They are only supposed to use lethal force to prevent immediate harm. I think society as a whole is ok with police lethal force.

The death penalty is still flawed. The jury of your "peers" is subjective and can easily be unjust. But I agree with it generally but the evidence would have to be overwhelming.

If you are on the battlefield and actively engaging against American forces you are fair game. John Walker Lynn for example. He was captured alive but if he had died it wouldn't have been an issue.

A more complicated killing is of Anwar al-Awlaki and his son. Both were Americans and neither were charged or convicted of a crime. The Obama Admin argued they were an imminent threat, they were killed in Yemen, and that justified their killing.

Awlaki was targeted. His son was 16 and the US official story was he wasn't targeted intentionally. They killed a few other children along with him.