Even in modern times, I think most don't realize how wacky Korean politics has been. For instance the president from 2013-2017 (Park Geun-hye, daughter of a former dictator) was involved in some sort of weird cult-like grooming controversy where she was being groomed and controlled by what some media called a 'Korean Rasputin.' She was eventually impeached and imprisoned for corruption/abuse of power, and is now serving decades in prison.
And it seems the current president of South Korea has an approval rating in the 30s. So I have no idea how Koreans view their government, but it's really unlike anything I think that we can compare elsewhere. But I suspect "trust" and "integrity" are not the sort of words that'd be on top.
I wish. It's a national tradition to jail and then pardon the president. She's been free for years, and is often kow-towing and gladhanding current administration members.
Although what I suspect will happen is that North Korea will fall apart eventually and South Korea will get a demographic surge from immigrating North Koreans.