Learn Hardcore Korean: hwayoireneun chinguwa hamkke chilpan apeseo balpyo yeonseubeul haesseoyo. - On Tuesday, I practiced a presentation with a friend in front of the blackboard.

-에는 combines the time particle -에 (“on/at”) with the topic particle -는, so it literally means “as for Tuesday.” It sets 화요일 as the topic of the sentence, often adding a nuance of contrast or emphasis (e.g. “On Tuesdays, (we at least) did X”). You could still say 화요일에 친구와 함께…, but 화요일에는 highlights the time more strongly.

What’s the difference between 에 and 에서 in this sentence? They both seem to mark location or time.

-에 marks a point in time or destination (here, 화요일에 means “on Tuesday”).
-에서 marks the place where an action occurs (here, 칠판 앞에서 means “in front of the chalkboard”).
So you need 에 for the time expression and 에서 for the location of the activity.

Why is it 친구와 함께? Could I say 친구하고 함께 or 친구랑 함께?

All three mean “together with a friend,” but differ in formality and register:

친구와 함께: more formal/literary (와 attaches to consonants).
친구하고 함께: neutral/informal (-하고 is colloquial).
친구랑 함께: very casual (랑 is a contracted form of 하고).
The meaning stays the same; choose based on your level of formality.

What does 칠판 앞에서 literally mean, and why use -에서?

칠판 앞 means “in front of the chalkboard.” Adding -에서 marks that location as where the action takes place. So 칠판 앞에서 = “at/in front of the chalkboard.”

Why is the phrase 발표 연습을 했어요 instead of just 발표했어요 or simply 연습했어요?

발표했어요 would mean “(I) gave/made a presentation” (the real thing).
연습했어요 by itself means “(I) practiced,” but you wouldn’t know what you practiced.
Combining 발표 (presentation) + 연습 (practice) + 을” + 하다 gives 발표 연습을 했어요 = “practiced the presentation.”

Is 발표 연습을 했어요 structurally a verb+object, or something else?

It’s a compound noun (발표 연습) plus the verb 하다 (“to do”). Grammatically:
1) 발표 연습 = noun phrase (“presentation practice”)
2) -을 = object particle
3) 했어요 = past polite of 하다 (“did”).
So you’re literally “doing presentation practice.”

There’s no subject like 저는 or 우리는 in the sentence. How does that work?

Korean often omits the subject when it’s obvious from context. Here, it’s understood as “I” or “we” (the speaker and friend). If you wanted to be explicit, you could start with 저는 화요일에는… or 우리는 화요일에는…, but it isn’t necessary.

Can I change the word order, for example put 칠판 앞에서 before 친구와 함께?

Yes. Thanks to particles, Korean is flexible. You could say:
– 화요일에는 칠판 앞에서 친구와 함께 발표 연습을 했어요.
– 화요일에는 발표 연습을 칠판 앞에서 친구와 함께 했어요.
The core meaning stays the same; moving elements just shifts the emphasis slightly.