Regarding the concept of "the prodigal son," how is it a parable for the idea of forgiveness?
I think that the parable goes very far to showing forgiveness and the idea that doors are never closed when there is love present. It speaks to the power of Jesus' teachings that the father holds out faith and belief in his son and never closes his door to him. The son leaves in an air of arrogance and ends up failing with his freedom because he leaves for all of the wrong reasons. The parable shows that parents who love their children, such as the love that presumably God has for us, never stop loving their children. In many ways, this is something that can be seen in worldwide religions regarding the idea of eternal forgiveness when one approaches the divine with folded hands and humility. When praying to the Mother Goddess in Hinduism, the saint Adi Shankaracharya says, "There is never a bad mother, only a bad child." This brings to light that children will always be welcome, such as the prodigal son who is welcomed by the father. The power of forgiveness allows us second chances and the possibility of redemption from our own misdeeds and poor uses of freedom.
I would add that the parable adds another dimension to the traditional idea of forgiveness. Here's the part that I find interesting:
"But while he was still a long way off, his father saw him and was filled with compassion for him; he ran to his son, threw his arms around him and kissed him.
It seems that his father was actually LOOKING for him because he was a LONG way off when his father saw him. He did not just see him as he walked into the house, or stepped on to the property, but when he was a long way off. In my reading, this indicates that he forgave him BEFORE he saw him. This is in keeping with the (frightful) injunction of the "Our Father" --- Forgive us our trespassers as [and only as] we forgive those who trespass against us." We actually ask to be forgiven as, and only as, we have forgiven those who have trespassed against us.
Given that standard, the father surely will be forgiven.