Many traditional Korean houses, which are more common in the countryside, have a small courtyard where children can play, and families can gather to wash vegetables or make kimchi.
This differs from household to household, but I've found that Korean children actually have fewer chores at home than what is typical in American culture. Korean children may be expected to help set the table or take out the garbage, but it is common for the mother or older family members to take care of the household overall.
Very common jobs in Korea are being an office worker, teacher or public servant. A huge part of the Korean economy are conglomerates. They employ a large part of the Korean population, and they are also considered very desirable jobs by the general population. Company and office jobs offer stability and prestige, two highly held values in Korean culture.
Education is considered one of the most important aspects of life. This is why middle schoolers and high schoolers have extremely long school days, often starting around 8:00 AM or 9:00 AM and ending between 6:00 PM and 9:00 PM.
Most students in Seoul get to school by walking or by bus. It seems that many, if not most, students in middle school and high school travel to school by themselves.