"A common greeting among Chinese is 'Have you eaten yet?' "

The chinese equivalent of "Hello" or "How do you do?" is ni hao (there is also "Good morning" and "Good evening", but they are rarely used). This greeting, however, is considered too formal to use with people that you know well (friends, colleagues, classmates, etc). There is no equivalent of the english "Hi" that can be used in this case, instead people begin with some innocuous questions such as "Where are you going?" or "Have you eaten yet?". One or two questions might serve to start a conversation, or they might in fact be the whole conversation if two people pass each other and want to say something, but don't have time to stop and chat. This is quite similar to the way that people ask "How are you?" in english, although it should be noted that in most parts of China people do not use this question as a greeting. (I say "most parts of China" because it so happens that in the place where I am now—Xining and the surrounding area—you do sometimes hear this greeting).

In books about chinese culture, you occasionally encounter the following explanation for the "Have you eaten?" question: during China's history, people often suffered from famines, or had to struggle to find enough food for their family, and hence the time of a person's previous meal became a very real and important topic. I don't believe this myth at all. The part about food shortage might be true, but China isn't the only country to have experienced famines over the last few centuries. More than ten percent of Ireland's population died during the famine of the late 1840s, but these days the Irish don't go around asking each other "How many potatoes have you eaten today?" When you consider the chinese habit of using a question as a greeting, and the fact that there are at least 7 or 8 hours of the day when you can reasonably ask "Have you eaten?", and add to this the importance of food and drink in chinese culture, it is no surprise that this question is so common.

Depending on the context—place, time, person, etc—there are lots of questions that can serve as greetings: "Have you got a class?", "Did you just finish class?", "Are you going to work?", etc. It's okay to ask questions where the answer is perfectly obvious, such as "Don't you have an umbrella?", or (when you see somebody coming out of their dormitory with a thermos) "Are you going to fetch water?". A one word answer is all that's required, and all that's expected. Somebody once asked me "Do you still live in the same place?" and I was a bit confused and gave them a very long answer. Afterwards, my friend who had heard the whole thing explained that it was just another kind of greeting, and an answer of "ng" would have been sufficient! In some situations, a greeting can just be a statement such as "You've come!" (or "You've come back!"), to which the person addressed can simply reply affirmatively: "I've come!"

"When your guest departs, you should see them to the front door of the building, or to the elevator at the very least."

Certainly this is true for formal visits, or the first time somebody visits you at home. The further you see somebody off, the more respectful it is. You might even see them to a bus stop and wait until a bus comes (for bonus courtesy points, try to pay for their fare!), and if they have a private car then you should wait until they have driven away before you turn around. The guest, in turn, should try to decline the courtesy by saying "No need to see me off!". Generally, you shouldn't say this until it is clear that the host is going to try to see you off—to say it earlier would seem presumptious.

Common farewells to a guest are "Goodbye", "Go carefully" (or "Drive carefully"), and "Come again". You can also say these to customers leaving a shop or restaurant.

If the person is a friend who has visited you a few times before, then you don't have to see them off. But to show that they haven't forgotten this courtesy entirely, people will often say "I won't see you off". To this, the guest should quickly reply "No need to see me off!", as if the thought had never crossed their mind.