Here's some details.
A: 숙젤 아직도 끝낸 게 없었어? (끝낸 게 없다 = "There's none that I've finished yet", not correct here)
B: 응. 만기일 다음 주 아니지? (만기일 is primarily a financial term. 마감일(formal), 마감날, or 제출일 is better)
* Also note the difference between these:
* 1. 다음 주 아니지? = It's not next week, right? (hoping to hear it's not next week)
* 2. 다뭄 주 아니야? = Isn't it next week? (= I think/thought it's next week)
* 3. 다뭄 주잖아? = It's next week, isn't it? (about the same as #2)
* Only #2 and #3 match your English version. #1 has the opposite meaning.
A: 오늘은 만기일이잖아! (오늘은 -> 오늘이. The main point is the homework. 오늘 is not the topic, so 이)
B: 진짜로?! Ugh (아이씨?). 망했어.
아이씨 is a medium strength expletive (like "Damn it!") expressing annoyance, not surprise as does "Ugh!".
For "ugh!", you can use one of these.
- 이이고 - widely used when you're surprised or flustered.
- 어 / 어어 - reaction of surprise (the end part must be raised. Otherwise, it means "yes").
- 어머 - Only used by women (but some men seem to use it these days).
- 악 / 억 - originally a sound of a scream, but it's used in everyday situation too for exaggeration or as a joke.
- 헉 - more recent variation of 악/억 which is popular.
The conversation might go like this.
A: 아직도 숙제 안 했어?
B: 응, 다음 주까지 아니야? / 응, 다움 주까지잖아? (= 다음 주까지 내는 거 아니야? 내다 = turn it in)
A: 아냐, 오늘까지야!
B (male version): 그래 / 진짜 / 헉? 아이고, 난 죽었다 [or 망했다 / 끝났다].
B (female version): 어머, 진짜? 어떡하면 좋아.