Can, for example, a fighter practice karate in Japan and represent Russia or any other country outside Asia in world karate championship?

Bon

You can practice/train anywhere, but whether you can represent Russia depends on the Russian World Karate Federation's (WKF) rules on who is eligibility. Many athletes in other sport train in one country, but represents another. For example, in tennis Maria Sharapova who was born in Russia, but trained in the US since she was 10 years old, represented Russia in the Olympics.