1. Law in Confucian countries, while no doubt updated to deal with modern circumstances, is basically an extension of 8th century Chinese law, so it is very different to any system in the modern West. For example, it is the state's paternalistic duty to promote virtue among the people, so any activity or thing deemed unvirtuous is banned: the highlights are various drugs, like opium, and various heretical doctrines like the White Lotus - 'heretical' being defined as anything which promotes vice, rebellion, disrespect for Confucian morals and social order, and lese-majeste. Each Confucian country's list of heretical doctrines is different depending on its local traditions and its interpretation of Confucian doctrine - Vietnam includes Christianity and Islam, while Korea includes Christianity and Buddhism. Being a missionary of the wrong religion is highly inadvisable. If you go to a random village, you may be treated to the sight of a local official standing in the village square and lecturing the assembled public about a particular law, along with stories to illustrate it, as part of the state's paternal duty to the people.
a. btw, if the Internet is a thing, these countries are 100% guaranteed to have a Great Firewall in order to minimize exposure to foreigners and the harmful doctrines they espouse, like democracy, feminism and human rights and so on. Expect a lot of anti-porn and anti-gaming regulation too - all in the name of promoting virtue, of course! If not for the fact that Christianity is probably banned, this would be a Christian conservative's wet dream.
2. Whipping is a very common legal punishment for light offenses. Conviction requires confession, and the magistrate is authorized to use torture; basically, just look up Japan's conviction rate and extrapolate from there. If you're a tourist, the government will not care when foreign countries protest over you getting roundly whipped on public television for something you didn't know was a crime. Every time a new emperor comes to the throne, the characters that make up his name are banned from public use, and lese-majeste laws are very much in force. There is also
an explicitly multi-tiered justice system in which some people get lighter sentences than others for the same crime -
except for certain crimes that not even the emperor is legally able to commute.
3. Confucianism is patriarchy incarnate, in the sense that men > women, family > everything else, father > his family, and this is baked into law in a way that can only be compared with sharia law in Islamic countries like Saudi Arabia or Iran. And just like how hardcore Christians can quote the entire Bible from memory, basically anyone in government or who wants to be part of government
absolutely must learn the Confucian canon by heart, otherwise he will not pass the civil service exam. And even if the civil service exam stops being mostly about quoting the Confucian texts as the country modernizes, you can bet your ass that being proficient in it is still going to be a requirement for passing it. This means that the only way to get ahead in society is to steep yourself in this doctrine, a lot like how all leaders in a theocracy must learn the holy text.
4. Confucianism, like any ideology, has competing branches. Generally, this competition is based around public debates and personality conflicts between the different factions, and is rather bloodless despite all the invective thrown around. Korea is different.
Korea is an ideological kudzu which was famous for having nasty purges happen like clockwork every 1-2 generations until one of the imperial in-laws basically took over the government and set his family up as the real rulers of the country in the 1800s. Of course, the ideological factions are still there; they just can't have each other executed for wrongthink anymore.
5. Absolute monarchy is the norm, though the power is mostly in the hands of the bureaucracy rather than the actual emperor. At most, the only form of "democracy" allowed is one where the
jinshi (people who passed the highest civil service exam) get to vote, because Confucian doctrine states that the educated, morally-cultivated person is inherently superior to the ignorant rube toiling in the fields.