The matching expressions are -나요? and -ㄴ/는가요?, or -거나요?(것이나요?) and -는 건가요?. -나요? and -ㄴ가요? are similar question expressions largely interchangeable. There is a theory that -나요 should be used for verbs and -ㄴ가요 for adjectives, as in 오늘 떠나나요? and 집이 큰가요?, but in practice few care about such a rule. There are some verb and tense combinations that make one or the other more natural in certain contexts though. For example, 이겼나요? seems a little more natural than 이겼는가요?, and 행복한가요? better than 행복하나요?, although this may be subjective and all four phrases are acceptable. As for -는 건가요?, it is a colloquial form of -는 것인가요?. It is more indirect because it has the inner phrase/clause anchored by -는 것. It has the subtle nuance of referring to that inner phrase as a distinct entity, as if observing or highlighting it, but the meaning is not that different in this case (There are other cases where -는 것이다 makes a greater difference). To summarize, - 집에 간다 (I'm/We're going home) -> 집에 가나요? / 집에 가는가요? (가나요 sounds better) - 집에 가는 거다 (no matching English phrase?) -> 집에 가는 거나요? / 집에 가는 건가요? (가는 건가요 is better) (거다 = 것이다, 거나요 = 것이나요, 건가요 = 것인가요) 집에 가는 거다 is like "It is that I am going home." structurally, but "It is that ..." is seldom used for this kind of ordinary meaning. So there doesn't seem to be a straightforward English translation of 집에 가는 거다.