Kuzenimin yeni kitabı masada.

Because it is built in steps:

• kuzen = cousin
• kuzenim = my cousin
• kuzenimin = of my cousin

The last -in is the genitive ending, which marks the possessor. In Turkish, when one noun possesses another, the possessor usually gets a genitive ending, and the thing possessed also gets a possessive ending.

So kuzenimin yeni kitabı is a possessive phrase meaning my cousin’s new book.

Because kitabı has a possessive suffix on it.

• kitap = book
• kitabı = his/her/its book, or in this kind of phrase, the book of ...

In Turkish possessive constructions, both parts are marked:

• kuzenimin = of my cousin
• kitabı = his/her book / the book belonging to that possessor

So Turkish does not just say my cousin book. It marks both nouns.

Not here. In this sentence, -ı is the 3rd person possessive ending, not the accusative.

A very common learner confusion is that the accusative and some possessive endings can look similar. The reason we know this one is possessive is the structure:

• kuzenimin is a possessor in the genitive
• the noun after it should take a possessive ending

Also, this sentence has no verb taking a direct object. It is a location sentence ending in masada, so there is no reason for an accusative object here.

This is a common sound change in Turkish called consonant softening.

Some nouns ending in p, ç, t, k change when a vowel-initial suffix is added:

• kitap → kitabı
• ağaç → ağacı
• kanat → kanadı
  and so on

Here, p becomes b because the suffix begins with a vowel.

So:

• kitap
  • -ı → kitabı

In Turkish, present-tense to be is often omitted in 3rd person sentences like this.

So instead of saying something like ... is on the table with a separate verb, Turkish simply says:

• Kuzenimin yeni kitabı masada.

This is completely normal and grammatical.

You do see forms of the copula in other situations, for example:

• Masadayım = I am at/on the table area
• Masadaydı = it was on the table

But in a simple 3rd person present statement, there is usually no separate word for is.

Masada is masa + -da.

• masa = table
• -da = locative ending, meaning in, on, at

So masada means on the table or at the table, depending on context.

The locative ending has several forms:

• -da
• -de
• -ta
• -te

The choice depends on vowel harmony and consonant voicing. Since masa has a back vowel and ends in a vowel, -da is the correct form.

Turkish word order is flexible, but the most neutral pattern is often:

topic/subject + predicate

Here:

• Kuzenimin yeni kitabı = the thing being talked about
• masada = the predicate/location

So the sentence naturally ends with the location.

A different order is possible, such as:

• Masada kuzenimin yeni kitabı.

That can sound more marked or emphasize where it is. But Kuzenimin yeni kitabı masada is the most straightforward version.

Because the owner is my cousin, not I directly.

Compare:

• benim kitabım = my book
• kuzenimin kitabı = my cousin’s book

In benim kitabım, the possessor is I, so the possessed noun takes the 1st person ending.

In kuzenimin kitabı, the possessor is the noun phrase my cousin. That whole possessor is treated as 3rd person, so the possessed noun takes the 3rd person possessive ending.

This is very normal in Turkish.

No. Yeni stays the same.

Turkish adjectives do not agree with nouns in gender, number, or case the way adjectives do in some other languages. So:

• yeni kitap = new book
• kuzenimin yeni kitabı = my cousin’s new book

The adjective simply comes before the noun and does not change.

Turkish does not have articles like English the and a/an.

Whether something is definite or indefinite is usually understood from context or from the grammar of the phrase itself.

In this sentence, the phrase is possessive:

• kuzenimin yeni kitabı

Possessive phrases are naturally specific, so English uses the in the translation, but Turkish does not need a separate word for it.

As a learner, you should treat that as not the correct form for this meaning.

For a normal possessive construction meaning my cousin’s new book, Turkish expects both parts:

• possessor in the genitive: kuzenimin
• possessed noun with possessive marking: kitabı

So the standard form is:

• Kuzenimin yeni kitabı

If you leave off the genitive ending, the sentence no longer clearly has the normal X’s Y structure.