No.
I'm pretty sure Turkey's in NATO, and they're part of Asia.
Yes, Tibet is a part of Asia, geographically Tibet lies in central-south Asia. It is smack-dab in the heart of Asia. If it isn't, nothing is.
Europe.
Svalbard is a part of Norway.
Vietnam is geographically on the borderline of east asia and se asia. Vietnam is the only country in se asia that can also be categorically part of east asia. Vietnam's people and culture is east asian, but geographically located in the borderline of se asia/east asia.
Greenland is geographically a part of North America, though politically a part of Europe. New Guinea is geographically a part of Asia, though it is politically split between the countries of Indonesia (Asia) and Papua New Guinea (Oceania).
Russia is a transcontinental country, spanning Europe and Asia. Geographically and politically it is a part of both. However, it is more geographically connected to Asia, and more politically connected to Europe. To help you better understand this, look at the United States. It is geographically a part of North America, but is much more politically a part of Europe, specifically Western Europe.
Turkey is the country that lies in both Europe and Asia. While most of its land area is located in Asia, the western part of the country is geographically considered part of Europe.
Svalbard is part of Europe, specifically belonging to Norway.
Svalbard is officially an archipelago which is the most northen part of Norway.
Asia and Europe are part of the same landmass, known as Eurasia. The boundary between Europe and Asia is somewhat arbitrary and culturally defined rather than geographically distinct.
Asia and Europe meet geographically at the boundary known as the continental divide, which runs through the Ural Mountains in Russia.