
I'm really enjoying this, but I have one question... If he is conscious in Yggdrasil, what is happening to his body in the real world? And what will happen if/when his real body dies? Will he to die? Or because the game has now become his "reality" will he continue to live in his new "body"?

Up to Volume 6 of the translated light novel, we don't know, but he's not in Yggdrasil anymore. He can smell, feel, and the NPCs think and speak; none of this was possible in the dive system Yggdrasil was played on.
There have been other players in the past of this world. They have become legendary figures in history, so we can reason that players were not brought into this world all at once, but rather staggered over time.
I have two main theories:
1. Upon shutdown, a full scan and backup was made of the game, including the brain pattern of any player still logged in. This data was saved and archived. Years, decades, or centuries later someone inserted this data into a new virtual world. A sophisticated AI could be managing this world, which is what interpreted the written settings of the NPCs and used that to formulate their personalities. Because any gaps in their settings seem to be filled with the personality of their creator, Yggdrasil may have had partial scans of all players who ever played.
2. A tool used for 10 years gains sentience, as a common Japanese myth goes. If such magic were real, what would happen to a game played by millions of people for 12 years? So much thought-energy might have actualized its existence into another plane upon server shutdown. Your World of Warcraft character might be alive in another dimension.
3. Don't think too hard, it's just a setup for a fantasy, "What if all my work in an RPG became real?"
Why hasn't anybody eaten the squirrel yet?