Does the President of Argentina live in a White House?

No, not specifically a White House. The official residence of the President is the Olivos Residence, a fairly large estate located in the neighbourhood called Olivos, just north of Buenos Aires. As for the government headquarters, just as the US has the White House, Argentina has a "Pink House". Yes, it's actually pink. Supposedly this color is due to it being painted long ago with paint colored with bulls' blood, a fairly common technique at the time. Gory indeed...