There are no countries currently a part of the European Union that are not a part of Europe. Cyprus is technically not geographically located in Europe, however, Cyprus is considered to be a part of Europe geo-politically. Cyprus is generally not included in Asia, as its tied to European politics.
To get a sense, take a look at the United States. The state of Hawaii is geographically located in Oceania, not North America. However, the US is not considered a transcontinental country, because Hawaii is generally not associated with Oceania politics. This is the comparable to the situation with Cyprus.
However, the European Union is looking to expand its borders and is considering to admit completely non-European countries, but Europeanized countries. Europeanized countries are countries that are similar in European culture, that being a Western Civilization. Israel is currently most likely to be this candidate in the future. Other Europeanized countries that the EU might look towards are Canada, the US, Australia, Japan, New Zealand, Morocco, etc. However, for the time being, the European Union is only looking to expand its borders inside Europe, particularly in the Balkans.
No. It is a country in Africa, not a country in Europe.
Albania is not a member of the organisation known as the European Union. It is a European country, being part of the continent of Europe.
Cyprus
No. That is not even possible.The European Union is an organisation, not a country. Europe is a continent, not a nation.
Ireland is a member of the European Union, and is in Europe.
No African country is a member of the European Union. 28 of Europe's countries are members. See the related question below.
Ireland is a European country and it is also a member of the organisation that is known as the European Union.
No, to be a member of the Eu your country must be in Europe. There is a country with a rather similar name -Austria. Yes, Austria is a member country and it is located in Central Europe.
European citizens retain the citizenship of their native country. They have relaxed travel restrictions to the rest of the European Union if their native country is a member of the European Union.
Yes, Cyprus is a member of the European Union.
No, Argentina is not a member of the European Union. Argentina is not in Europe, it is in South America.
Yes. Norway is a country in Europe. It is not a member of the organisation known as the European Union, as many countries aren't, but it is still in Europe, so Norwegians are European.