A1: 학교에서 몇 시에 수업이 시작해요? (questionable sentence) B1: 9시에 수업을 시작해요. A2: 몇시에 수업이 끝나요? B2: 오후 1시에 수업이 끝나요. There are 수업을 and 수업이 because 시작하다 is both transitive and intransitive verb, while 끝나다 is strictly intransitive. In the sense it's used here, I believe 시작하다 is transitive in its most common usage, as it is used in B1. However, some people use it like an intransitive verb too like A1. This dual usage is the reason you see two different particles. Personally, I find A1 not so natural (also refer to http://tip.daum.net/question/92347154/92347155). Note that we have 시작되다(vi - something starts) and 시작하다(vt - to start something), as well as 끝나다(vi) and 끝내다(vt). If we're to follow the [S+Vi] pattern, A1 should be written as 수업이 시작돼요?, which is the same as A2 structurally. In real life, however, 시작해요 is used a lot more in this situation, although not like A1. We typically say (학교에서) 수업 몇 시에 시작해요? or 학교 수업은 몇 시에 시작해요 when asking. When answering we rarely say 수업을, but just say something like 9시에요, or 수업 9시에 시작해요 when answering in full. It's a difficult subject because it's not clear how widely sentences like A1 are used. I think you can just make a note that수업(을) 시작해요, 수업이 시작돼요, and 수업이 시작해요 are all possible.

이 and 을 never combine because they mean opposite things 이 is a subject marker 수입이 끝나요 The class ends. 을 is an object marker 수업을 시작해요. (I) start class. Here, the (I) is not explicitly stated because in Korean they often don't repeat the subject/object You could additionally say 수입이 시작돼요. But this means "Class begins"

I think that must be a mistake. It should be 수업이. "수업을이" is ungrammatical, as it uses both object and subject-marker.