Traditional Chinese culture is something so wide and variational that it is hard to write about. China was suspect to Civil War so often in ancient times that entire ethnic groups and people’s were wiped out of existence, only for them to spring back into existence a few years later. Although this is the case, there are some customs and umbrella terms under traditional Chinese culture.
Buddhism is something that China all throughout its history has had wide popularity. It is something that one may see almost everywhere they go when touring the place. Another popular traditional Chinese culture is Taoism or The Way, which started as simply a way to live life, but transformed into, maybe because of Buddhism, a full-fledged religion. Confucius, the 5 virtues of a good government, also is a large part of traditional Chinese culture and is one of the reasons that the Communist government of China is so widely popular among the Chinese themselves (until recent years) especially to the older generations. Those are the main points I saw in traditional, non-westernized Chinese culture.
When saying, “I’m sorry,” to anyone in Chinese culture, there are several ways to apologize to to them, but body language-wise you should do a motion similar to waving with both your hands as well as bowing you head while apologizing. This is more commonly done which people of similar ages though. Another motion you can do is holding your hands in front of you and bowing your head or nodding your head. That’s the best explanation I can give in that respect.