Argentinia
It is Argentina.
Argentina in the Falklands thusly named the Falklands War
Argentina is closest.
Argentina
China
Argentina is the nearest.
Argentina
The short answer: yes. The Falklands were owned by the British, and they still are. This was why the war broke out, as the Argentinians believed that they had the best claim to ownership of the islands.
Argentina
Probably the Falklands - although technically they are a group of islands, not a country.
Depending on where you are, the nearest communist country could be almost any South American nation, Russia, China, Vietnam or Cuba.