You have raised a very complex issue! How land masses are classified as continents depends on whether you are a geologist or a geographer. Martin Lewis, in The Myth of Continents, says, "Continents are understood to be large, discrete masses of land ideally separated by expanses of water." However, many of the seven most commonly recognized continents are identified by convention rather than by
1) adhearance to the ideal criterion that each be a discrete land mass, separated by water from others (note Europe and Asia) or
2) inclusion of the shallow, submerged adjacent area (the continental shelf) and the islands of the shelf
I think we should go with the 7-continent model based on convention since it is the model usually taught in most English-speaking countries . That is: N. America, S. America, Antarctica, Africa, Europe, Asia, Australia. Australia is defined by geologists as the Australian mainland, New Guinea, Tasmania, and the small intervening islands, all of which sit on the same continental shelf, but is defined by the Australian Government as just mainland Australia. For simplicity's sake, and again to be consistent, we should just include mainland Australia as a continent.
New Zealand is not on the same continental sehlf and is not part of Australia but part of a wide region know as Oceania (not a continent). Now the 5 oceans is another matter, In 2000, the International Hydrographic Organization created the fifth world ocean - the Southern Ocean - from the southern portions of the Atlantic Ocean, Indian Ocean, and Pacific Ocean. The Southern Ocean completely surrounds Antarctica.
Hope this helps -
Mirla Morrison