I'm intrigued by your questions. I'm not sure how to answer them satisfactorily but here goes.
1. Luke records 19 parables not found in the other Gospels. This is also true of the other writers. Not all of them tell the same stories. There is no simple answer. It may be helpful to study Luke's purpose, readers, style, emphases etc. Have you read or studied the Synoptic Problem. This would be helpful. How do we explain the similarities and the differences if there are common sources?
2. Parables usually make a single point. This parable is one of three in Luke 15 that deal with the grace of God in seeking and saving what was lost. The lost sheep and the lost coin stress the work of God in the search for what is lost. and the subsequent joy when found. The third looks at the experience of the lost but it is underlined by the unfailing love of the father in welcoming home the lost son.
While the third is set in a family context it is not about family but about the father's love for the lost son. All three parables are a stinging rebuke to the Pharisees who, in their self righteousness legalism, despised sinners. It is part of Jesus' running debate with the Pharisees on the nature of salvation; is it by works or by grace? In illuminating the character of our Heavenly Father. Luke apparently did not think it necessary to include the mother.
3. There are interessting parallels of the grace of God to each but since there is neither reference nor allusion to Jacob I doubt if Luke has him in view. Luke is writing to a Gentile, mainly Greek audience. Jewish history would be of little help there.
4. I think that the robe, the ring, the shoes and the welcoming feast all indicate a complete reconciliation and restoration of sonship.
5. There are many paradoxes in the Christian faith. The tension between grace and justice is only one of them. Others would be the tension between love and fear. We are to both love and fear the Lord.
There is tension also between God's Sovereignty and Human Responsibility. We like things to be simple, black and white, but it simply is not that way. The older I become the more I see the paradoxes as not only a mental challenge but, more importantly, a great means of growth in plumbing the depths of the Grace of our Lord Jesus Christ.
I pray that this is of some help to you. It has been a privilege to interact with you.