안녕하세요, 아린씨, Mr. Park has already explained the second and the third question quite well. There is nothing for me to add. Maybe I can say something more about the first question. verb stem + 으니 means "since, because, and so". There is a cause and effect relationship, obviously sequential. The first part leads to the second part. Some simple examples: 시간이 없으니 이만 가겠습니다. Since there is no time, I will just leave now. 몸이 불편하니 집에서 쉴래요. My body aches, so I think I will stay home today. Let's take a look at your example. 그런데 주택 말이 나왔으니 부탁하는 건데요..... This part loosly translated means "Since the subject of housing came up I have a favor to ask, The last part: 김영수 씨, 저에게 하숙집을 구해 주실래요? Mr. Kim YS, would you mind finding a boarding house for me? We could put these two parts together by removing the 요 and 김영수 씨, but they have a purpose. The 요 and calling his name shows that this favor is important to her and not bing asked lightly. "As long as we are on the subject of housing, I have a favor to ask... Mr. Kim, would you mind finding a boarding house for me?" "Speaking of housing, I have a favor to ask... Mr. Kim, would you mind finding a boarding house for me?" I hope I did not confuse you! :)

1. 말이 나왔으니 -으니 : 앞말이 뒷말의 원인이나 근거, 전제 따위가 됨을 나타내는 연결 어미 -으니 means "because" same to "기 때문에" 말이 나왔으니 = 말이 나왔기 때문에 means because it was mentioned 2. 건데요 건데요 is a short form of 것인데요. 것인데요. is composed of 것이(다) + -ㄴ데 + 요. 것이(다) means "something to do" -ㄴ데 : 해할 자리에 쓰여, 어떤 일을 감탄하는 뜻을 넣어 서술함으로써 그에 대한 청자의 반응을 기다리는 태도를 나타내는 종결 어미. -ㄴ데 is an ending particle has a nuance of adding exclamation and waiting response from the listener. 요 is honorific particle. 부탁하는 건데요 means "That is something to plead" or "That's why I'm pleading" 3. ㄹ래요 generally means "do you want to" but ~해 주실래요 means "would you do ~ " 저에게 하숙집을 구해 주실래요? means Would you look for lodgings for me?

This person is saying that they have been told that new places to live are available and they want to know if a reservation can be made for them. "Would you do" is polite form of speech. "Do you want to" is OK but less polite. It seems to me that being polite is very important here if the speaker wants 김영수 씨 to help them. 김영수 씨 (Kim Sooyoung) is a woman's name so 으니 could be mispelled 언니. 언니 means older sister and shows respect. This is a fun study. Thank you!