Yes, I agree those two sentences are perfect and have the same meaning.

No, they don't mean the same. A. Americans in China are often asked about things they regard as private, means that people ask Americans questions on topics which the Americans regard as private matters (the implication being, they shouldn't be asked those questions). "B. Americans in China are often asked about what they regard as private" means that Americans are asked "what topics do you regard as private matters (the inference being, once we understand what topics are off limits to you, we will make sure we don't ask you those sort of questions".

Thank you for your comment.

Yeah, you could use both and still convey the same meaning

Yeah, you could use both sentences