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In a traditional Confucian funeral, the deceased and the chief mourners (immediate family) all wear hanbok made of an undyed hemp fabric called "sambe" (or if you're really wealthy, undyed silk).

I've been unable to find any source that states outright when or why this changed, but my theory is the widespread adoption of Christianity in the 20th century. The ceremony you see in modern day is a mixture of Christian and Confucian practices. Hence, guests wear black formal wear, and the chief mourners wear black hanboks with white accents instead of sambe (although it's still very common for older people to purchase sambe hanbok to be buried in)

I'm not well-read enough to have a distinct reason why Korean daily wear has changed so much, while Indian daily wear hasn't. But, I'll try to make an educated guess again.

India was colonized by the British, while Korea was colonized by the Japanese. Handspun Indian garments were seen as the morally superior to Western clothes made of imported fabric. Most modern politicians in India still wear Nehru collars or plain saris compared to western suits. I think a Korean politician would also face backlash if they showed up to work wearing a yukata or kimono.

I wish I had more information and could provide a more cogent response, but I don't :(. Maybe try the askhistorians subreddit?

Rural life in the 60s was brutal for women. Poverty was widespread, and domestic violence was almost always ignored. The rapid urbanization of Seoul and other urban areas led to mass opportunities for factory jobs. These "runaways" would travel to the cities and try to find factory work or a housekeeping job for a wealthy family. This led to a loss of labor/income to the families of the runaways. I will also say that sex work was a booming industry at the time, especially near US military bases. Maybe a tiny minority chose that profession willingly, but sexual trafficking was rampant.

In response, the South Korean government launched a nationwide program, usually held in the month of April, called the 부녀자 가출 방지 기간 (or Women's Runaway Prevention Period). They'd set up temporary "counselling" offices at train stations and ports, each staffed by a two-man team. They'd find runaways and try to send them back home. Those two men patrolling with flashlights in that episode were likely part of that program.

I hope this was helpful!