Learn Hardcore Korean: suyoiredo sueobeun ojeon 10sie sijakhaeyo. - Even on Wednesday, class starts at 10 a.m.

-에 is the basic time/location particle meaning “at” or “on.” When you add 도, it becomes -에도, which means “also at/on” or “even at/on.”
So 수요일에도 literally means “also on Wednesday” (or “even on Wednesday”), implying that something happens on Wednesday in addition to other days.

Why is 수업 marked with 은 instead of the subject marker 이/가?

은/는 is the topic marker. It introduces 수업 (“class”) as the topic of the sentence and often adds a contrast or emphasis. Here it sets up “as for the class(s)…”
If you used 수업이, you’d simply mark it as the subject without that topical or contrastive nuance: 수업이 오전 10시에 시작해요 means “The class starts at 10 AM,” stated neutrally.

Why do we say 오전 10시에? What role does -에 play with time expressions?

In Korean, the particle -에 attaches to time nouns to indicate “when” something occurs (“at” a certain time).
오전 10시 means “10 AM,” so 오전 10시에 means “at 10 AM.”

What speech level is used in 시작해요, and how is it different from 시작합니다?

시작해요 is the polite informal (or “요-form”) speech level, used in everyday conversation with people you’re not very close to.
시작합니다 is the formal polite (or “합니다체”) level, used in more official or formal settings. Both are polite, but -해요 is slightly less formal than -합니다.

Can I change the word order to 수업은 오전 10시에 수요일에도 시작해요?

Korean word order is relatively flexible thanks to particles. While that sentence is grammatically correct and understandable, putting 수요일에도 at the very end shifts the emphasis. The original fronted 수요일에도 highlights “Wednesday” first. The alternative sounds more like an afterthought.

Why is there no explicit subject like “we” or “they” in this sentence?

Korean often omits subjects when they can be inferred from context. Here it’s clear you’re talking about “the class” or “classes,” so there’s no need to say 우리가 or 그들이. Omitting it makes the sentence more natural.

Could you use 에도 on 수업 instead, like 수업에도 수요일에 오전 10시에 시작해요? What would that mean?

Putting 에도 on 수업 (수업에도) would mean “even the classes” or “classes too,” which changes the focus. 수업에도 implies you’re including classes among other things (e.g., meetings, events). That’s a different nuance: “Even the classes start at 10 AM on Wednesday,” rather than “(As for) the classes, they start at 10 AM on Wednesday too.”