Christians you believe that by killing gods son we are redeemed?

Well I see it like this you were convicted of a crime and you were going to be sentenced to death. I had compassion on you and wanted you to have a chance of a better life so I go to the judge and i say, "please do not execute this man please take my life instead and let him go free I will pay his debt." I believe God created the world and everything in it and he was so kind he gave man a free will to decide if they want a relationship with him or not. Sin entered the would through Adam and Eve and God looked down at his creation and saw that they were doomed because they could do nothing to eradicate there sin so he offered a sacrifice in that his son came to earth as a man then went to the cross as a sacrifice for the sins of the world present past and those to come. He died and then defeated death and rose again and ascended to heaven again with his father. Once and for all he paid the price for the sins of men and to receive that gift you must believe in the Lord Jesus Christ and confess that you have sinned and believe that he has taken the burden of your sin away and you must live your life as a pardoned individual. Long but i hope you understand what i believe.

I guess he took the punishment for sins instead of us?

How can a heathen make sense of or understand Christianity? We?