wǒ yòng qiānbǐ xiě zhōngwén zuòyè.

Because Mandarin often uses this pattern:

Subject + 用 + tool/instrument + verb + object

So in this sentence:

我 + 用 + 铅笔 + 写 + 中文作业

literally: I + use + pencil + write + Chinese homework

This is a very common way to say what tool you use to do something.

Examples:

• 我用笔写字。 — I write with a pen/pencil.
• 他用手机看视频。 — He watches videos on his phone.

English often says with a pencil, but Mandarin commonly uses 用铅笔 = use a pencil.

Yes. That is a very natural translation.

Even though 用 literally means to use, in sentences like this it often corresponds to English with:

• 用铅笔写 = write with a pencil
• 用筷子吃饭 = eat with chopsticks
• 用中文说 = say it in Chinese / use Chinese to say it

So learners should not translate word-for-word too rigidly. In this sentence, 用铅笔写 naturally means write with a pencil.

Because 中文作业 is treated as a noun phrase in which 中文 directly modifies 作业.

So:

• 中文作业 = Chinese homework
• 英文老师 = English teacher
• 数学书 = math book

In Mandarin, 的 is often omitted when the modifier and noun form a close, common combination.

Compare:

• 中文作业 — Chinese homework
• 我的作业 — my homework

You usually would not say 中文的作业 here. That sounds less natural for this meaning.

In practice, it usually means Chinese homework, that is, homework for Chinese class or homework related to the Chinese language.

Depending on context, it can mean:

• homework for your Chinese class
• homework written in Chinese
• an assignment involving Chinese

In real life, context tells you exactly which nuance is intended.

Good question. In Mandarin, both 做作业 and 写作业 are common, but they are used a little differently.

• 做作业 = do homework
  This is the broad, general expression.
• 写作业 = write homework
  This is especially natural when the homework involves writing.

So 写中文作业 is very natural, because Chinese homework often involves writing characters, sentences, or answers.

Examples:

• 我在做作业。 — I’m doing homework.
• 我在写作业。 — I’m writing homework / doing written homework.

In this sentence, 写 works well because the tool 铅笔 is mentioned.

It is possible, but 我用铅笔写中文作业 sounds more natural.

Why?

• 做作业 focuses on the activity of doing homework in general.
• 写作业 matches better with 铅笔, because a pencil is specifically used for writing.

So:

• 我做中文作业。 — I do Chinese homework.
• 我用铅笔写中文作业。 — I write Chinese homework with a pencil.

The second one is the better match for this sentence.

Here, 中文 functions as a modifier before the noun 作业.

By itself, 中文 can mean:

• the Chinese language
• Chinese writing/text
• Chinese class/subject, depending on context

In 中文作业, it works like an adjective-like modifier:

• 中文作业 = Chinese homework

Mandarin often lets nouns modify other nouns directly without changing form.

The basic sentence is very natural as it is:

我用铅笔写中文作业。

Mandarin word order is somewhat flexible, but not completely free. The usual order here is:

subject + 用-phrase + verb + object

You may also hear:

• 我写中文作业，用铅笔写。 — I do Chinese homework, using a pencil.
• 中文作业我用铅笔写。 — As for Chinese homework, I write it with a pencil.

But for a learner, the original order is the safest and most standard.

Sometimes, yes.

Mandarin often drops subjects when they are already clear from context. So in conversation, someone might simply say:

用铅笔写中文作业。

This could mean:

• write Chinese homework with a pencil
• I write Chinese homework with a pencil
• (You) use a pencil to write Chinese homework

The subject is omitted only when context makes it clear. In a basic textbook sentence, 我 is usually kept.

Because no noun here is being counted.

Measure words are needed when you specify a number or demonstrative before a noun, for example:

• 一支铅笔 — one pencil
• 这支铅笔 — this pencil

But in 用铅笔, the sentence just says use pencil / use a pencil, not one pencil or this pencil, so no measure word is needed.

The same is true for 中文作业 here. It is just Chinese homework, not one assignment.

The common measure word is 支.

So:

• 一支铅笔 — a pencil / one pencil
• 那支铅笔 — that pencil

Example:

• 我用一支铅笔写中文作业。 — I use a pencil to write Chinese homework.

Not exactly, though they are related.

• 中文 often refers to the Chinese language, especially written Chinese, or the school subject Chinese
• 汉语 usually refers more specifically to the Chinese language, especially in linguistic or teaching contexts

In this sentence, 中文作业 is the natural choice.
汉语作业 is possible, but it sounds more formal or textbook-like.

So for homework/class contexts, 中文 is very common and natural.

Yes, they matter a lot. Mandarin tones change the word.

The pinyin here is:

• wǒ
• yòng
• qiānbǐ
• xiě
• zhōngwén
• zuòyè

If you ignore tones, people may still understand you from context sometimes, but your pronunciation will be much less accurate.

For example:

• wǒ is third tone
• yòng is fourth tone
• zhōng is first tone
• wén is second tone

It is best to learn both the syllables and the tones together from the beginning.

Because Mandarin does not use articles the way English does.

So:

• 铅笔 can mean a pencil, the pencil, or pencils, depending on context
• 中文作业 can mean Chinese homework, the Chinese homework, or sometimes Chinese homework assignments

If you want to be more specific in Mandarin, you usually add other words, such as:

• 一支铅笔 — a pencil
• 这支铅笔 — this pencil
• 那个中文作业 — that Chinese homework assignment

Without those words, the meaning stays general and context fills in the rest.