Translation:What is the most famous animal in China?
Because in the most basic scenario, adjectives (e.g. "有名") used as subject complements in Chinese are essentially stative verbs and contain the concept of "to be".
Or you can think of "有名" even more directly as a verb phrase meaning "to have a name", so this sentence translates to something like "China's what animal most has a name".
I don't know. Really it's "What animal of China's is the most famous", as it doesn't specify where it's famous, and the likely intended meaning is "most famous around the world". We can get away with using "in China" to describe the animal, but I think your suggestion shifts the idea to suggest that there's an animal from who-knows-where that's the most famous in China. i.e. among residents of China.