Question: What is it that gets reborn?
Only the body is born. If the mind is not cleared of its previous impressions, it keeps watching the scene, what we call in spiritual terms 'drishya'. So then it gets attached to a body. Thus the conscious appears to get re-born and re-born. Finally when the consciousness is cleared completely, then there is no more re-birth.
Question: When that happens, is there individuality remaining?
Actually when this happens, no individual is left. All the droplets have become one with the ocean. But as the body is retained, then work is performed in this world, and proper manners should be followed. For instance it is proper manners to say, "Shivabalayogi is my Guru and I am His disciple."