मैं पत्र लिख रही हूँ, और वह लड़की पत्र पढ़ रही है।

Because रही shows that the speaker is female.

In Hindi, the present continuous is built like this:

main verb stem + रहा / रही / रहे + form of होना

So:

• लिख रही हूँ = am writing said by a female speaker
• लिख रहा हूँ = am writing said by a male speaker

So मैं itself does not tell you the speaker’s gender, but रही does.

It would be:

मैं पत्र लिख रहा हूँ, और वह लड़की पत्र पढ़ रही है।

Only the first continuous participle changes:

• female speaker: लिख रही हूँ
• male speaker: लिख रहा हूँ

The second part stays the same because लड़की is feminine, so पढ़ रही है is already correct.

Because लड़की is a feminine singular noun.

In this kind of sentence, the participle agrees with the subject:

• लड़का पढ़ रहा है = the boy is reading
• लड़की पढ़ रही है = the girl is reading

So in वह लड़की पत्र पढ़ रही है, the word रही matches लड़की.

Here, वह means that in वह लड़की = that girl.

But वह can also mean he, she, or it, depending on context.

Examples:

• वह लड़की = that girl
• वह पढ़ रही है = she is reading
• वह लड़का = that boy / he

So वह is a very flexible word. When it comes before a noun, it often works like that.

Hindi usually prefers Subject–Object–Verb order, while English usually uses Subject–Verb–Object.

So:

• English: I am writing a letter
• Hindi: मैं पत्र लिख रही हूँ
  • मैं = I
  • पत्र = letter
  • लिख रही हूँ = am writing

The main action usually comes near the end in Hindi.

The second clause works the same way:

• वह लड़की पत्र पढ़ रही है
• literally: that girl letter reading is

That is normal Hindi word order.

Hindi has no articles like English a, an, and the.

So पत्र can mean:

• a letter
• the letter

The exact meaning depends on context.

If you want to make a/one letter more explicit, you can say:

• एक पत्र = a letter / one letter

So both of these are possible:

• मैं पत्र लिख रही हूँ = I am writing a letter / the letter
• मैं एक पत्र लिख रही हूँ = I am writing a letter

Yes, Hindi can use a pronoun, but repeating the noun is also very natural.

Your sentence says:

मैं पत्र लिख रही हूँ, और वह लड़की पत्र पढ़ रही है।

This can mean that each clause simply mentions a letter.

If you specifically want to say the girl is reading it / that same letter, you could say:

मैं पत्र लिख रही हूँ, और वह लड़की उसे पढ़ रही है।

Here:

• उसे = it / that / him / her, depending on context

Hindi often repeats nouns where English might prefer a pronoun. So the original sentence is not strange.

They are forms of the verb होना = to be, and they help form the present continuous.

In this sentence:

• मैं ... लिख रही हूँ
• वह लड़की ... पढ़ रही है

The endings are:

• हूँ with मैं = am
• है with वह लड़की = is

So:

• लिख रही हूँ = am writing
• पढ़ रही है = is reading

A very useful pattern is:

• मैं ... हूँ
• तुम ... हो
• वह ... है
• हम/वे ... हैं

Because पत्र is the direct object, and in this sentence it does not need को.

Hindi often uses को with:

• people
• animate objects
• specific objects in some contexts

But with many inanimate direct objects, especially in simple non-perfective sentences like this, को is usually omitted.

So these are normal:

• मैं पत्र लिख रही हूँ
• वह किताब पढ़ रही है
• मैं पानी पी रहा हूँ

Using को here would usually sound unnatural.

The structure is:

verb stem + रहा / रही / रहे + form of होना

In your sentence:

• लिख
  • रही
    • हूँ = लिख रही हूँ
• पढ़
  • रही
    • है = पढ़ रही है

The choice of रहा / रही / रहे depends on gender and number:

• रहा = masculine singular
• रही = feminine singular
• रहे = masculine plural or respectful/plural contexts

Examples:

• मैं लिख रहा हूँ = I am writing (male)
• मैं लिख रही हूँ = I am writing (female)
• वे पढ़ रहे हैं = they are reading

It is correct, but it can sound a bit formal or textbook-like in modern everyday speech.

Other common words are:

• चिट्ठी = letter
• ख़त = letter, often in an Urdu-influenced register

So in everyday conversation, people may more often say:

• मैं चिट्ठी लिख रही हूँ।

But पत्र is still a perfectly valid Hindi word, especially in formal writing, school materials, and official contexts.

Yes, depending on context, English may translate it as that girl or sometimes simply the girl.

Hindi does not have a separate word exactly like English the, so वह can help point out a specific person or thing. In context, translators may choose:

• that girl
• the girl

So वह लड़की पत्र पढ़ रही है could be understood as:

• That girl is reading a letter
• or, in natural English depending on context, The girl is reading the/a letter

The exact choice depends on the situation, not just the grammar.