If you compare Vietnam War with Korean War, you can notice there is one difference between them. Vietnam is a name of the country while Korean is an adjective relating to North or South Korea or its people or language. You don't call the war in Vietnam Vietnamese War because it is the way it is as the Ngram Viewer clearly shows.
However, both compound nouns carry the same characteristic. The two wars were fought by Vietnamese and Korean people respectively within the boundaries of each country even though they were supported by other countries such as the former USSR, China and the U.S., etc.
- Star Wars simply means multiple (more than two) wars among (fought by) stars. The compound noun is made in the same way as Vietnam war and Korean War. Then, why not starry war like Korean war? The word starry according to Online Oxford Dictionary doesn't have the right connotation as it means:
Full of or lit by stars, resembling a star in brightness or shape, or
(informal) relating to stars in the world of entertainment
The producers and director chose Star Wars as they can choose whatever they like with their artistic licence also known as poetic license. It is up to them to choose among Star Wars, Wars of Stars, Wars of the Stars and Starry Wars, etc. Therefore, your second question is not very meaningful, but I would say it is equivalent to Wars of Stars
World War is compounded in the same way as Vietnam War or Korean War. The war was fought by many countries almost all over the world, not in one specific country. Then, why not Worldly War? Because people decided to call it World War and it was used by many people.
As explained in the other post, we can make compound nouns (or noun phrases) that include a noun modified by adjectives or noun adjuncts. And the noun adjuncts (first noun) are used as if they were an adjective. That's why only the second noun takes the plural form as in Star Wars.
You can visit the following Wikipedia link to learn more about compound nouns.
Edit: The noun adjuncts World and Vietnam can mean the places where the wars were fought. The World War was fought in many countries in the world. That's why it is called World War. The Vietnam War was fought in Vietnam. That's why it is called Vietnam War.