I think you have several questions here. One of them is whether the US justice system is working well, and I would say it's a big system and more goes on than I know about, but it doesn't feel like it's working very well.
Another question you have is whether forgiveness and the death penalty go together, and there are many questions wrapped up in that. Forgiveness doesn't mean saying it's okay that wrong was done, and it doesn't mean no consequences. And not all the consequences are in this life. Also who is forgiving whom? You can't forgive wrong done that was not done against you (though when a person is murdered, everyone is wronged to some extent by being deprived of that person). Forgiveness is about not holding a wrong against someone, not seeking revenge, not trying to get back at them. You can forgive someone who abused you, and be kind and friendly to them (not holding it against them), but yet refuse to be alone with them (consequences). Consequences and revenge are often intertwined, which is why there is so much confusion about forgiveness, but they are not the same thing.
God said right after the Flood that man is special because of being made in God's image, and that therefore any man or animal that kills a man is to die (consequence). You could still forgive, and many have forgiven (not held it against) their murderers even as they were dying. But there are still consequences, ordained by God, that put such a value on human life that the man who takes it loses his own right to it.
I recommend the recent movie "Amish Grace" as a very good exploration of how forgiveness, love, and justice work together.