Australia isn't a continent - it's part of the continent of Asia, as is the Marshall Islands. To distinguish it from mainland Asia, the region of Australia and the surrounding states is sometimes referred to as Oceania - whether the Marshall Islands sits in that region or not varies according to different sources.
Part of the Marshall Islands are a part of the US. (The islands of Bikini and Enewetak use to be US nuclear test sites.)
No.
The Marshall Islands were sold to Germany and became part of German New Guinea.
Islands in an ocean don't belong to any continent. If they were part of a continent they wouldn't be islands would they? The African Continent is the continent nearest the Canary Islands, but the islands are the result of volcanic activity on the ocean floor.
Asia
Tasmania
The Shetland Islands, which are part of the United Kingdom, are in the continent of Europe.
Tori Shima islands are part of Japan, making them part of the continent of Asia.
The Caribbean islands are part of North America.
New Zealand is an Island Nation and not a part of any continent.
Bikini Atoll is part of the Marshall Islands in the Pacific Ocean.
Alaska is part of the North American continent. Hawaii is a chain of islands in the Pacific Ocean, so it is not considered to be part of any continent. Instead, it is part of Oceania, a region centered on the islands of the tropical Pacific Ocean.