A great way to make money? They don't pay you to live with you, or at least from my experience when my sibling was on exchange program in the past.
I think there is no way to do it you become an exchange student in Korea, too. In other words, she lives with you here, then you live with her there.
Unlike Universities, I think high schools do not have the program where they just come live with you, and you don't go there to study.
However, I may be wrong since the rules and programs may have changed, and it is probably different with every education board system.
1. True. My family has hosted exchange students (high school age) five times over the span of over ten years: three times for one school year and two times for about one month. We didn't get paid for it, as far as I can remember, or rather we got only enough to cover the student's expenses if they stayed for a year and nothing at all if just for a month or so. It's NOT a way to make a significant profit, generally.
2. False. I never went to study in any of those students' home countries. I wasn't even in high school yet when we hosted the first three students. They just came to the U.S. and my family provided a place to stay. Also, my high school had a two-way exchange with a Japanese "sister" high school, but hosting a Japanese student for about a month didn't mean that the student from my high school was absolutely required to go to Japan the next year. Same for the time some German students came and visited on exchange for a while, since that was only a one-way exchange.
As for what it's like, it depends on the exchange student you get. My family had three exchange students we really liked and felt like they were part of the family by the time their time with us was up. A couple of them even came back to visit, and one even brought his whole family back with him to see us! On the other hand, one of the kids we hosted didn't always follow my parents' rules (possibly less likely to be a problem with a Korean student than with an Italian one? because he was used to a ton of freedom at home), and the last guy we hosted was when I was actually in high school myself, but he was sort of stand-offish at times and wasn't too warm. He just didn't hit it off with anyone in my family, was kind of picky, a bit reserved, and didn't seem to like the U.S. much. He was still OK, though. Overall, I would rate our experience with exchange students as generally positive, with some really wonderful experiences. The students come to learn about your country, but you learn a lot from them, too.
As the host family, you have the upper hand, really, because it's your home, your country, and your rules that the exchange student has to work around. If you're an only child, though, I hope you understand what it's like to have another kid living in your house for an extended period of time. Exchange students will take up some of everyone in your family's time and energy. I had two exchange students when I was pretty young and a brother of my own, so it wasn't really hard for me. Exchange students are sort of between a guest and a family member if they live with you for a whole year.
I don't know how well a Korean exchange student would speak English, because most high school and college arrivals from Korea seem to be pretty bad at it. All of our students were from Northern, Western, Central, or Southern Europe (Netherlands, Sweden, Italy, Austria) and pretty good at English, which I definitely think helped with communication. If you speak Korean then it won't be an issue, but it's not necessarily a good thing to speak to an exchange student in his/her native language all the time and feed him/her food from their native country, because the main point of a homestay is to be immersed in another culture.
Oh, and I didn't mind the fact that four out of our five exchange students were guys when I was younger, but it was kind of strange having a random guy my own age living in my house for a month when I was in high school (I'm a girl). You might want to request an exchange student of the same sex. I really enjoyed having another high school-age girl living with me for a while.
