To your point #1, I think this is a good case for restricting...not limiting, the death penalty. The standard for conviction is beyond a reasonable doubt, but I would be fine with imposing beyond a shadow of a doubt standard for the DP. Use it only in cases such as the Ted Bundys, the night stalkers, the John Wayne Gacys where there is no doubt whatsoever.
As to point 2, I really dont see that repentance is a state function, so from that standpoint it is irrelevant. I do believe God will forgive a repentant murderer, even at the point of execution. But that does not change the earthy consequences of ones actions.
I love Catholics, they are my brothers and sisters in Christ. But this pope is a fine example of why I could not be one. He is a man and not infallible...and although some would say that the infallibility only extends to doctrine, this example, or his stances on illegal immigration, or socialism show how easily ANYTHING can be dragged into the arena of doctrine.