Does the President of the United States of America actually live in the White House?
The President does live in the White House although he may choose to have a residence elsewhere that he owned before becoming President. Bush had his ranch back in Texas that he visited often. Of course, there is also the official retreat at Camp David where the President takes time off. As for your PM, there IS an official residence for him. The Prime Minister’s official residence is The Lodge in Canberra, but not all Prime Ministers choose to make use of it and your current PM may be one of those.