A big part of Chinese culture is tea. In Confucianism, the eldest are to be seated first and get all sorts of perks relating to respect. As the youngest at my table (one month decides everything), I poured tea for the whole table. If you are the oldest at a table, you are pretty much waited on hand and foot by the rest of the members of your party.
The two-fingered gesture here was brought into being by Emperor Qianlong of the Qing Dynasty. On his travels to South China, he poured the tea of a servant and the servant, because he was bound to an oath to not reveal his master's identity, he did the gesture to symbolize bowing.
This again symbolizes respect for your senior, in this case, it is in status rather than age, since the gesture was originally made from a servant to the emperor himself.
There are many obscure parts of Chinese etiquette that are relatively unknown, including an aversion to the number four, symbolizing death. In this example, there is a superstition that chopsticks may never be put straight down into a bowl of rice; doing so would bring death to the table.
In this dumpling, there is sweet paste. However, unsuspecting diners will bite into it, and it will explode!
This particular dish symbolizes the Daoist element of wu-wei, or non-action. If you perform an action- such as biting into the bun- it will explode. However, going with the flow and not doing anything will allow you to eat the bun without yellow paste all over you.
Fun fact: These are not carrots.
They're dumplings! Spontaneity is a part of Daoism. In this case, it is a surprise, and it's a disguise- like an animal that conceals itself as its prey's food, so this is an allusion to nature.
While the outside of this design is Confucian, its inside is inherently random, making it Daoist.