Yes. It ran for 70 years, with a truce during WWII. It was called the Cold War. It was fought in Korea, Vietnam, and many other countries.
> why you're this eager to minimise the crimes of Nazism.
I'm not eager to "minimise" anything. Nazis were horrible, but Communists killed more people, and that is just a fact. Why are you so eager to defend Communism?
> it's for you to show that Kim Jong-Un is a Communist
Umm... no, it isn't up to me to prove something that's been common knowledge since the 1950s, namely that North Korea is a Communist regime.
The DPRK was notionally Communist in the Leninist mold originally, but it was progressively recast into what its own propaganda describes as an alternative Socialism/Communism, but which expressly rejects Marxist materialism and the central role of economic relations with a central role of the individual and the single great leader. In many ways, it's more Fascist than Communist in substance (the highly centralized ideology of Juche bearing an analogous relation to the heirarchical Fuhrerprinzip as absolute monarchy does to feudalism.)
Has there been a world war against the communists? Not that I am aware - your comparison of WW2 and the Cold War is false although I appreciate that you're only doing it to try and force an argument to the extremes.
(You also might want to reflect on why you're this eager to minimise the crimes of Nazism.)
> Can you give me an example of a Communist country that isn't a dictatorship?
I don't need to - it's for you to show that Kim Jong-Un is a Communist and a handful of collective farms doesn't really get you there.