What is the nature of the individuals relationship with the ultimate reality to Hinduism and what is unique about the way that this relationship is approached in Hinduism?

Either Monist or Dualist: you are the Ultimate Reality, or you can become the Ultimate Reality. These viewpoints are to some degree limited to the schools of Hinduism growing out of classical philosophical positions and may or may not be relevant to a Hindu practitioners depending upon their particular creed - Hinduism is just as big and just as diverse as Christianity.