Learn Hardcore Japanese: eiga no serihu wo nooto ni kaite nihongo no benkyou wo simasu. - I write movie lines in my notebook to study Japanese.

台詞 (せりふ) in kanji feels a bit more formal or literary, and you’ll see it in books, subtitles, and more serious writing.
セリフ in katakana is very common in everyday writing, manga, casual text, etc. It feels a bit lighter or more conversational.

Meaning-wise, they are the same: “(spoken) lines, dialogue, a line (in a play, movie, etc.).”
In this sentence, you could write 映画のセリフ and the meaning would be unchanged.

What is the role of を after 台詞? Is it the object of 書いて or of 勉強をします?

The を after 台詞 marks 台詞 as the direct object of 書いて (write).

Break the sentence:

映画の台詞をノートに書いて
→ (I) write the movie lines in a notebook
日本語の勉強をします
→ (I) do Japanese study

So:

台詞を ← object of 書いて
日本語の勉強を ← object of します

Japanese allows multiple を in one sentence if they belong to different verbs in different clauses, as here.

Why is に used after ノート (ノートに)? Could I use で or へ instead?

Here, ノートに marks the target location where something is written:

ノートに書く = to write in / into a notebook

Particle choice:

に
Used for the destination / final location of something being put/written:
- ノートにメモを書く = write notes in a notebook
- 紙に名前を書く = write your name on the paper
で
Marks the place where an action happens:
- 学校で勉強する = study at school
  You might say something like ノートで勉強する (“study using a notebook”), but not ノートで書く to mean “write into a notebook.”
へ
Mostly used with movement verbs (行く, 来る, 帰る, etc.) for direction.
It’s not used with 書く in this meaning.

So ノートに書く is the natural and standard way to say “write in a notebook.”

What does the て-form in 書いて do here? Does it mean “and”, “then”, “while”, or “in order to”?

The て-form (書いて) connects actions, and its exact nuance depends on context. Basic possibilities:

Sequence: “write … and then …”
Simple conjunction: “write … and …”
Means/manner: “(I) study Japanese by writing movie lines”

In this sentence:

映画の台詞をノートに書いて日本語の勉強をします。

the most natural interpretation is means / method:

“I study Japanese by writing movie lines in a notebook.”

You could expand it to something like:

映画の台詞をノートに書いて、日本語の勉強をします。
→ “I write movie lines in a notebook, and (in that way) I study Japanese.”

So it’s closest to “and (as a way of)” or “in order to” in English, but grammatically it’s just the standard て-form connection.

Why is it 日本語の勉強 and not 日本語を勉強 in this sentence?

Both patterns are common and correct:

日本語を勉強する
→ “to study Japanese” (verb + object)
日本語の勉強をする
→ “to do study of Japanese” / “to do Japanese study” (noun + の + noun + する)

In your sentence:

日本語の勉強 is a noun phrase meaning “study of Japanese.”
Then をします = “do (it).”

Nuance:

日本語を勉強します feels a bit more direct and simple.
日本語の勉強をします slightly emphasizes the activity “study” as a thing you do, like “I do my Japanese study.”

In everyday speech, both are natural; choice is mostly style and rhythm.

Why is there を after 勉強 (勉強をします)? Isn’t 勉強する already a verb?

You’re right that 勉強する is a verb meaning “to study.”

Structurally:

勉強 is a noun (“study” as an activity).
勉強をする = “to do study” → “to study.”

Over time, 勉強する has become a single, very common verb. When you say 勉強をする, you’re literally saying “do study”, with 勉強 as the object of する and marked by を.

Both forms are correct:

勉強する / 勉強します
勉強をする / 勉強をします

Nuance:

勉強します is a bit shorter and more common.
勉強をします can sound slightly more deliberate or formal, but the difference is small.

Is the subject “I” here? Why is there no explicit subject in the sentence?

Yes, in most contexts this sentence would be understood as “I”:

(私は) 映画の台詞をノートに書いて日本語の勉強をします。
(I) write movie lines in a notebook and study Japanese.

Japanese frequently omits the subject when it’s clear from context (who is speaking, previous sentences, situation, etc.).

You only need to say 私 (or another subject word) when:

you want to introduce or contrast who does the action, or
the subject could be ambiguous.

Otherwise, dropping it is more natural.

Can I change the word order, for example by moving 日本語の勉強をします earlier in the sentence?

You can reorder some parts, but not freely like in English. The verb phrase (here 勉強をします) normally comes at the end.

Original:

映画の台詞をノートに書いて日本語の勉強をします。

Natural variations:

映画の台詞をノートに書いて、日本語の勉強をします。
(Just adding a comma/pause.)

You can move the shorter phrases around before the verb, for example:

日本語の勉強を、映画の台詞をノートに書いてします。
→ Grammatically possible but sounds awkward/unusual.

In practice, the original word order is the most natural:

Describe how you study (映画の台詞をノートに書いて)
Then say what you do (日本語の勉強をします)

Could I say 映画の台詞をノートに書いて日本語を勉強します instead? Is there any difference?

Yes, that’s perfectly correct:

映画の台詞をノートに書いて日本語を勉強します。
→ “I write movie lines in a notebook and study Japanese.”

Comparing:

日本語の勉強をします
→ “I do Japanese study.”
日本語を勉強します
→ “I study Japanese.”

Nuance difference is very small:

The の + 勉強 version emphasizes the activity “study” as a noun.
The を勉強する version is a more straightforward verb + object.

Both are natural and would usually be understood the same way in this context.

Could I say 書いてから instead of just 書いて? What difference would that make?

Yes, you could say:

映画の台詞をノートに書いてから、日本語の勉強をします。

書いてから explicitly marks sequence:

書いてから = “after writing (them), …”

Nuance:

書いて日本語の勉強をします
→ “I study Japanese by writing movie lines in a notebook.”
(method / looser “and then / and” connection.)
書いてから日本語の勉強をします
→ “First I write the movie lines in my notebook, and after that I study Japanese.”
(clearer first X, then Y sequence.)

In real-life use, the original sentence without から is often interpreted as ‘by doing X, I do Y’, i.e., method of study. Adding から makes it sound more like two separate steps in time.

How would this sentence change in casual or more formal speech?

Base sentence (polite):

映画の台詞をノートに書いて日本語の勉強をします。

Casual version:

映画の台詞をノートに書いて日本語の勉強をする。
Or even shorter: 映画のセリフをノートに書いて日本語を勉強する。

Changes:

Drop ます → する (plain form).
Often also drop を after 勉強 (勉強する).

More polite / formal:

映画の台詞をノートに書いて日本語の勉強をいたします。
(いたします is the humble form of します, used in very polite contexts like customer service, speeches, etc.)

The structure and particles stay the same; only the verb ending changes according to politeness level.