1. 오늘 만날 수 없어요. 요즘 너무 바쁘잖아요. I would say as follows. 오늘 만날 수 없을 것 같아요. 요즘 너무 바빠가지고요. First, the literal translation for "I'm not able to meet you today" is the one you wrote for sure, but most Koreans don't really use conclusive remarks. They almost always soften their words even though it's something certain. Secondly, for the latter half, if you use -잖아 like you did, then people might think that you being busy is something they're already informed. They might consider it as "아시다시피(As you know) 제가 요즘 너무 바쁘잖아요". Just putting it like "요즘 너무 바빠서요" would be a most neutral(?) choice, I guess. And -가지고요 is the same with -것 같아요. It just allows them to avoid the conclusive remarks. 2. I would say "정답이 아니잖아요. 어제 공부 안했어요?" The correct location for '안' should be right in front of the main verb, but the way you put it is not that much of an error, children make that kind of mistakes sometimes. And for the '맞는 대답', your translation would be fine, but I strangely feel more offended when you put it that way other than 정답. It's really slightly little tho. 3. I would say "잊어버렸죠?" because "잊어버리나 봐요" means "I assume you always forget". It sounds sarcastically. 4. Typo, I guess? "저에게 왜 해변에 가고 싶었는지 물어봤어요?" will do. But I would say like "왜 해변에 가고 싶었는지 물어보셨나요?" in colloquial conversations. 스웨터 사야했어요... I mean it works but... I would say just "스웨터 사질 그랬어요?" or "대신 스웨터 사시지..." Because "사야 했어" feels kinda imperative, so it doesn't go well with the honorific suffix. But you can always use "사야 했어" to the close friends or family members. (1 )At least it's warm = 적어도 따뜻해 = 적어도 따뜻하긴 해 = 그래도 따뜻하잖아? = etc... (2) 스카프로도 따뜻해 = The scarf is warm enough.