(a) Let the judge decide.
(b) Obviously there are cases where guilt is proved 100%. e.g. clear video evidence. Or a guilty plea.
Like I said, concerns about putting the wrong person to death aren't relevant where the person is clearly guilty. Then it becomes a question simply of, ought this person be punished by being put to death for a crime of this seriousness?
(c) I don't think you're right here. Otherwise why would Parliament keep debating the death penalty frequently?
Article 2 says "1. Everyone's right to life shall be protected by law. No one shall be deprived of his life intentionally save in the execution of a sentence of a court following his conviction of a crime for which this penalty is provided by law." The words I have put in bold seem to allow a state to impose the death penalty, in fact. But correct me by all means if I have misinterpreted this.