लेखक ने यह जीवनी लिखी।

ने marks the subject of many perfective transitive verbs in Hindi.

Here, लिखी means wrote, which is:

• perfective: the action is completed
• transitive: it has a direct object, यह जीवनी (this biography)

So Hindi says:

• लेखक ने ... लिखी = The author wrote ...

This is a very common pattern in Hindi:

• राम ने किताब पढ़ी। = Ram read a book.
• सीमा ने चिट्ठी लिखी। = Seema wrote a letter.

This use of ने is often called ergative marking.

In this kind of sentence, the verb often agrees with the direct object, not with the subject.

The direct object here is जीवनी, and जीवनी is feminine singular. So the verb takes the feminine singular form:

• लिखी = feminine singular
• लिखा = masculine singular

That is why we get:

• लेखक ने यह जीवनी लिखी।

Compare:

• लेखक ने यह लेख लिखा।
  Here लेख is masculine, so the verb is लिखा.
• लेखक ने यह किताब लिखी।
  Here किताब is feminine, so the verb is लिखी.

You usually learn the gender of each noun as part of the vocabulary. In this sentence, we can also tell from the verb agreement:

• जीवनी is feminine
• therefore the verb appears as लिखी

Many Hindi nouns ending in -ी are feminine, and जीवनी is one of them. But this is a tendency, not a perfect rule, so it is still best to learn noun gender individually.

Because यह is the direct form of this, while इस is the oblique form.

Here, जीवनी is a direct object without a postposition, so the direct form is used:

• यह जीवनी = this biography

You use इस when a postposition follows:

• इस जीवनी में = in this biography
• इस जीवनी को = this biography (with को)
• इस जीवनी पर = on this biography

So:

• यह जीवनी लिखी is correct
• इस जीवनी लिखी is not correct in standard Hindi

Hindi does not always mark direct objects with को.

In this sentence, जीवनी is an inanimate direct object, and leaving it unmarked is completely normal:

• लेखक ने यह जीवनी लिखी।

With को, the object can sound more specifically marked or emphasized in some contexts, but with inanimate nouns like जीवनी, Hindi very often uses no को at all.

A rough guide:

• animate / persons are more likely to take को
• inanimate things often do not

So this sentence is natural as it stands.

Yes. This follows the very common Hindi pattern:

• Subject + ने + Object + Verb

So:

• लेखक = subject
• ने = subject marker in this tense/aspect pattern
• यह जीवनी = object
• लिखी = verb

Hindi word order is more flexible than English, though. You may also hear:

• यह जीवनी लेखक ने लिखी।

That can shift emphasis, but the basic neutral order is:

• लेखक ने यह जीवनी लिखी।

Traditionally, लेखक is the masculine form for writer/author, and लेखिका is the feminine form.

So if you specifically want to say a female author wrote this biography, you would often say:

• लेखिका ने यह जीवनी लिखी।

However, in modern usage, some masculine profession words are also used more generally in certain contexts. Still, for learners, it is safest to understand:

• लेखक = male author / masculine form
• लेखिका = female author / feminine form

That is one of the key features of Hindi grammar in the perfective with many transitive verbs.

When the subject takes ने, the verb often does not agree with the subject. Instead, it agrees with the direct object, as long as that object is not blocked by something like को.

So here:

• subject: लेखक ने
• object: यह जीवनी (feminine singular)
• verb: लिखी agrees with जीवनी

This is why the sentence does not use masculine लिखा, even though लेखक is masculine.

Here, यह means this.

In Hindi, यह can also function as a third-person pronoun in some contexts, roughly like this one / he / she / it, depending on the situation. But in this sentence it comes directly before a noun:

• यह जीवनी = this biography

So here it is clearly a demonstrative adjective, not a standalone pronoun.

In careful transliteration, यह is often written yah, but in everyday speech it is very commonly pronounced closer to yeh.

So learners often hear:

• yeh jeevani

Both the spelling tradition and the spoken pronunciation are worth knowing:

• written transliteration: yah
• common spoken form: yeh

The same kind of thing happens with वह, often pronounced more like voh in speech.

In standard Hindi, with a completed transitive action like wrote, ने is normally required.

So the standard sentence is:

• लेखक ने यह जीवनी लिखी।

Without ने:

• लेखक यह जीवनी लिखी
  would sound ungrammatical or nonstandard in ordinary Hindi.

So for learners, the safest rule is:

• with a transitive verb in the perfective, use ने on the subject

Then the verb would usually switch to the masculine form.

For example:

• लेखक ने यह लेख लिखा। = The author wrote this article.

Here:

• लेख is masculine singular
• so the verb is लिखा

Compare:

• जीवनी feminine singular → लिखी
• लेख masculine singular → लिखा

This is a very useful pattern to notice in Hindi perfective sentences with ने.