Some cultural practices get expanded upon in Rise of Kyoshi, especially the Fire Nation. As Rangi is teased about her topknot in the group, Kyoshi recalls that sometimes after an important Agni Kai, the loser would shave parts of their head bald, symbolizing "an extra level of humility from their defeat". Which does explain why Zuko's hair looked the way it did in book one.
Another reason why Kyoshi's daofei group are called the "Flying Opera Company"? Not only do they dust-step which allows them to appear like they're flying in the air, they also used to use a bison to travel.
Jessa likely carried fans as her weapons since they were easier to conceal than an airbending staff.
Why did Xu Ping An's lightning attacks did very little damage to Kyoshi after the initial strike aimed at her hands? He was aiming her torso, which was protected by the concealed chainmail inside her dress — or in other words, she was safely inside a Faraday's cage, protected from the electric current.
The traditional Earth Kingdom methods to find the next Avatar didn't work because Kyoshi's parents were leaders of a group of daofei bandits named the Flying Opera Company, which was constantly traveling around the Earth Kingdom. The old methods did work — it's just by the time the authorities got there to check it out, Kyoshi's family was either long gone or concealed in a secret daofei hideout.
Though we only see how two nations find the Avatar, it is still quite clear why they use their methods instead of the other. The Earth Kingdom uses geomancy, which cuts the world in half, then that half in half, so on and so on until they end up at the Avatar's door. This works great for the Earth Kingdom, where people generally stay in the same village for generations. But it would never work with the Air Nomads, who are constantly moving. So the Nomads instead have children pick toys; this doesn't work in the Earth Kingdom because they have a massive number of towns (and the kids are greedy instead of monks), but it's a simple matter for the Nomads, who only have four permanent settlements.
Why are the vast majority of the daofei non-benders? The daofei are mostly Forced into Evil, those who for whatever reason can't find work in legitimate society. Benders have more employment opportunities, so they're less likely to fall in with that crowd. But if they do, they can quickly rise to leadership positions by brute force.
As is traditional for the series, both Avatars shown start out as what the world didn't need: Kuruk was a partier and entertainer when the world needed a stable symbol, and Kyoshi was a meek servant when the world needed a judge. And related, Yun was a diplomat in an era where no one was interested in playing by the rules. While he of course wasn't a real Avatar, if he had been he likely would have evolved into a judge similar to Kyoshi.
Xu Ping An holds an impossible power that makes him one of the most powerful people in the world, is able to inspire legions of followers, was thought lost for years before returning unexpectedly, and considers himself the guardian of the world. He is essentially the daofei Avatar, and thus it is fitting that the real Avatar is the one who finally kills him.
In the series, the Kyoshi warriors and Kyoshi island have as much influence from Japanese culture as they do from Chinese culture like most of the rest of the Earth Kingdom. As the Fire Nation seems mostly to be based on Japan, this seems slightly odd. We now can see why, which is that Rangi was involved in the early days of the Kyoshi warriors.
Back in "The Southern Air Temple", we see a flashback where Aang says the monks might have made a mistake in identifying him as the Avatar. What initially seemed to be simply Aang's self-doubts now take on a new meaning with the reveal that the wrong person had been identified as the Avatar in the somewhat recent past, something Aang was probably aware of. Thus, Aang's doubts retroactively became a legitimate argument.
