In China, finishing all the food in a meal is considered to be rude

The reason this is regarded as impolite is because, in their view, this implies that the host did not provide enough food and you are still hungry!

It is also important to remember to use communal chopsticks for serving yourself food - using your own personal chopsticks to do is basically the equivalent of "double dipping."

You're not supposed to point your chopsticks at other people, or stick your chopsticks vertically into a bowl of rice. However, talking with your mouth full, burping, and putting your elbows on the table are all ok.
(Sources: 1, 2)