He was born here and is an American citizen just like any other child born here regardless of the nationality of the parents (diplomatic personnel). No you can’t assume he renounced his American citizenship. There are specific rules about that.http://travel.state.gov/law/citizenship/citizenship_776.html You got proof that he did those things? The different rules link your post also makes the point that he’s a US citizen by birth. It’s in the section Citizenship by being Born in the United States.
As for the Wong Kim Ark case I’ll bet there are many superseding cases. That case was decided in a period where we were trying to exclude all Chinese from becoming citizens and severely limited their rights in ways that no current court would or should. The court also in this case held he was in fact a citizen of the United States and couldn’t be kept out (last paragraph).
Why did he come as a foreign student. Fox’s answer in their broadcast was that he wanted the full scholarship that was being provided to foreign students. If he was a US citizen he wouldn’t have been eligible. Basically he committed fraud to get the scholarship.
His farther was not a diplomat when the child was born so the diplomatic exclusion would not apply.