Learn Hardcore Japanese: kanozyo ha zutto kazi wo site ite, hiruma no benkyou ga sukosi okureta. - She was doing housework the whole time, so her daytime study got a bit behind.

彼女は marks the topic: “as for her…”. It sets the stage and makes the sentence about her situation.
You could say 彼女がずっと家事をしていて…, but が would emphasize that it was specifically “she (and not someone else)” who was doing the housework—more focus on the doer rather than the topic. It can sound contrastive or answer an implicit “who?” question.
In neutral narration, 彼女は is more natural.

What exactly does ずっと mean here? How is it different from いつも?

Here ずっと means “continuously” or “for a long stretch (of time).” It describes an unbroken span during which she was doing housework.
いつも means “always/usually,” i.e., a habitual tendency, not necessarily one continuous block.
Note: ずっと can also mean “by far” in other contexts (e.g., こっちのほうがずっと安い), but here it’s the “continuously” meaning.

What’s going on with していて? Why not していた?

していて is the て-form of している (progressive/resultative), used to link clauses: “(she was) doing housework, and…”.
The て-form can imply a natural flow or cause: “(since/while) doing housework, (as a result)…”.
していた would close the clause and make a separate sentence or require another connector: 彼女はずっと家事をしていた。昼間の勉強が少し遅れた。 The original with していて、 feels smoother and shows the connection.

Can I drop を in 家事をしていて?

Yes, in casual speech you can say 家事していて. With する-verbs, を is often optional in conversation.
家事をしていて is slightly more careful/formal and is the safer default in writing.

Does the て-form here mean “because”? Could I use ので or から?

The て-form can carry a causal nuance in context: …していて、(so)….
You can make the cause explicit:
- Matter-of-fact: 彼女はずっと家事をしていたので、昼間の勉強が少し遅れた。
- More personal/subjective: 彼女はずっと家事をしていたから、昼間の勉強が少し遅れた。
- Formal: …していたため、…
- Negative/blame nuance: …していたせいで、…

Why is 勉強 marked with が? Why not 勉強を遅れた?

遅れる is intransitive: the thing that is delayed is the grammatical subject, marked by が.
- 電車が遅れた (The train was delayed)
- 会議が遅れた (The meeting was delayed)
- 昼間の勉強が遅れた (The daytime study fell behind)
If you want a transitive “to delay something,” use 遅らせる: 勉強を遅らせた (she delayed her studying).

Isn’t the subject “she”? Why does it switch to “study” in the second clause?

彼女は is the topic, not necessarily the subject of every clause. In the second clause, the grammatical subject is 昼間の勉強 (her daytime study).
Think: “As for her, (she was) doing housework for a long time, and (as a result) her daytime study fell a bit behind.”
The “her” is understood: 彼女の昼間の勉強 (ellipsed possessive).

Why 昼間の勉強 and not 昼間に勉強?

昼間の勉強 forms a noun phrase “daytime study,” which then becomes the subject of 遅れた.
昼間に勉強 is not a noun phrase; it’s an adverbial time phrase modifying the activity of studying. To keep the same meaning, you’d need to nominalize: 昼間に勉強するのが少し遅れた (heavier/wordier).
The original is concise and natural.

Could I say 昼間の勉強は少し遅れた instead of が?

Yes. は would topicalize and often imply contrast: “As for the daytime study, it fell a bit behind (implying, for example, that other study didn’t).”
が simply marks it as the subject and states the fact without contrastive nuance.

What’s the difference between 遅れた and 遅かった? Which should I use here?

遅れる = “to be delayed, to fall behind” (event/process subject with が).
- 宿題の提出が遅れた (The homework submission was delayed)
遅い = “late/slow” (adjective). 遅かった is its past form: “was late/slow.”
- 反応が遅かった (The response was slow/late)
For schedules, arrivals, falling behind, use 遅れる (as in the sentence). For describing slowness/lateness as a property, use 遅い.
For being late to an appointment/class: 授業に遅れた or 授業に遅刻した (遅刻する is “to be late” as a discrete act).

Does していて … 遅れた imply “had been doing”? How is past perfect handled?

Japanese doesn’t have a dedicated past perfect form. The sequence (past-progressive background) … result in past conveys the English “had been … and then …”.
ずっと家事をしていて、…遅れた naturally reads as “She had been doing housework (for a while), so her study ended up behind.”
You could also use していたので to make the background explicit.

How would I make the sentence polite?

Can I use ちょっと instead of 少し? Any nuance difference?

Both mean “a little/a bit.” ちょっと is more casual and often softens statements; 少し is a bit more neutral/formal.
Here both are fine: 少し遅れた (neutral) / ちょっと遅れた (casual).

What’s the nuance difference between 昼間 and 昼?

昼間 (ひるま) emphasizes “daytime” as a span (as opposed to nighttime).
昼 (ひる) often means “noon/midday” but can also mean daytime in general. 昼間 more clearly contrasts with night and can feel broader as a period.
In this sentence, 昼間の勉強 highlights the daytime block of studying.

Where can I place ずっと? Is 家事をずっとしていて okay?

Both ずっと家事をしていて and 家事をずっとしていて are acceptable.
Placing ずっと before the noun-verb chunk (ずっと家事をしていて) is the most common; moving it right before the verb (家事をずっとしていて) can slightly stress the continuity of the action itself. The difference is minor.