'Nearer' compares two things so you need to give a choice. You need to tell the listener which two things they should compare. "Is London or Amsterdam nearer to Paris?" If you mean of all the rivers in the world, use 'the nearest'. This compares more than two things. "Which river is the nearest to the Yangtze?" By the way, because the Yangtze is a river, I'd say "Which OTHER river is the nearest to the Yangtze?"

I'm not a teacher at all, but am a native speaker. As others have said, your sentence can be correct if you give extra information before hand. For example... Lets consider the Nile and the Thamas. Which river is nearest to the Yangtze. That is fine. So yes, in some situations it is fine, but not on its own. However I personally would use "closest" rather than nearest. There is nothing wrong with nearest, but I guess it sounds more natural to me, so.. Lets consider the Nile and the Thamas. Which river is closest to the Yangtze. That sounds very good to me :)

The sentence is not grammatically correct. It should be: "Which river is nearer to the Yangtze?" However, the sentence might sound more natural if you add some context or specify the rivers you are comparing. For example: "Which river, the Yellow River or the Han River, is nearer to the Yangtze?" This provides more clarity and helps readers or listeners understand the comparison you are making.

Which (requires two or more rivers) is closest to the river Yangtze. by saying closest to "the river Yangtze" you are making it clear you mean the river Yangtze, otherwise "the Yangtze" is undetermined not qualified and could be anything or any place. "which of the following there rivers is closest to the river Yangtze. 1 The river Thames 2 the Mississippi river 3 the river Nile. And pay attention to whether locals and/or map makers etc say "the river x" or "river x"

Grammatically the sentence is correct if we know that we are talking about the Yantzee and two other rivers. However I am not sure it makes sense logically. How do you measure "the" distance between two rivers? Rivers are not point locations. The sources of the Mississippi and Missouri rivers are 1500 kilometers apart, but the rivers join near St. Louis. So their distance is 1500 km at one place but zero at another. Here is an example that is both grammatically and logically correct: "You can see the Statue of Liberty from New York City or Jersey City. Which city is nearer to the Statue of Liberty?"