I'm a little confused... He is the Prime Minister right? So why doesn't he live in the Blue House and why is he…
South Korea has both a President and a Prime Minister. The President is elected by the people and the Prime Minister is chosen by the President. The PM is in charge of the other ministries. More about it on Wikipedia (http://en.wikipedia.org/wiki/Government_of_South_Korea#Executive_branch) if you're interested.