In Western culture, we can nod our heads up-and-down for "yes" and shake them left-and-right for "no". Does Chinese have anything similar, or do they do the same thing? Are there other gestures for "yes" and "no"?

It is the same in China and Chinese culture we nod our heads (up-and-down) to say "Yes" and shake our heads (left-to-right) to say "No". There are no other gestures to say "Yes" or "No". However, to indicate you agree with someone or something, you can also say "en" while you are nodding you head. Now question for you: Are you finding this answer helpful? I hope you'd see "en" while you are nodding you head :)