"How do you know what happens after death?"
Based upon my belief of scriptures and God working in my heart.
"Can you show this to be true?"
No. Faith is the assurance of things hoped for. If we were around an altar and I called fire down from heaven and God listened to my prayer, you wouldn't believe it came from God. And you know it. Until you ask God to forgive your sins and step out in faith will you understand this to be true.
"Why would He punish us for doing something that He has designed into us to do?"
God can't stand sin. He designed us KNOWING we would fall but He didn't design us WANTING us to fall.
"If God knew what David would do, and He still created David, how did David have a choice?"
God design for David's life does not stop David from making the choice he made nor does it stop God from knowing and guiding David through those choices.
"Could David have done something that God knew he would not do?"
Right, we each have differing faiths.
Why would God design us in a way He didn't want us to be?
If David could not do otherwise, then where was his freedom of choice?