Ben onun kitabını masaya koyuyorum.

Yes, ben can be omitted.

Turkish often leaves out subject pronouns because the verb ending already shows the person.
Koyuyorum already tells us the subject is I.

So both of these are possible:

• Ben onun kitabını masaya koyuyorum.
• Onun kitabını masaya koyuyorum.

Using ben can add emphasis, contrast, or clarity, like I’m the one putting it on the table.

This is a very typical Turkish possession pattern.

• onun = his / her / its
• kitabı = his/her/its book
• kitabını = his/her/its book as a definite direct object

Turkish usually marks possession in two places:

1. the possessor gets a form like onun
2. the thing possessed gets a possessive ending, here kitabı

So:

• onun kitabı = his/her book
• onun kitabını = his/her book with object marking added

This is called the genitive-possessive construction.

Because that is how Turkish normally builds an explicit possession phrase.

If you say onun, Turkish expects the possessed noun to carry the matching possessive ending:

• onun kitabı = correct
• onun kitap = wrong

So the pattern is not optional decoration. It is the normal structure for his/her book, my car, their house, and so on.

Examples:

• benim evim = my house
• senin araban = your car
• onun kitabı = his/her book

Sometimes yes, if the context already makes the possessor clear.

But kitabını by itself can be ambiguous. Depending on context, it can mean:

• his/her book as the object
• your book as the object

So onun kitabını is clearer.

Turkish often omits the possessor if it is obvious from context, but including onun removes doubt and can add emphasis.

Because kitap changes to kitab- before a vowel-initial suffix.

This is a common Turkish sound change called consonant softening:

• p often becomes b
• ç often becomes c
• t often becomes d
• k often becomes ğ or g

So:

• kitap
  • a vowel-starting suffix → kitabı...

That is why you get:

• kitabı
• kitabını
• kitaba

not kitapı, kitapını, or kitapa.

That n is a buffer consonant.

The noun first gets the 3rd person possessive ending:

• kitabı = his/her book

Then it gets the accusative ending. When Turkish adds a case ending after a 3rd person possessive form, it usually inserts n first:

• kitabı
  • accusative → kitabını
• kitabı
  • dative → kitabına
• kitabı
  • locative → kitabında

So the n helps connect the possessive form to the next ending.

Because it is the specific direct object of the verb.

In Turkish, a definite or specific direct object usually takes the accusative ending. Here, it is not just a book in general. It is his/her particular book.

So:

• onun kitabını koyuyorum = I am putting his/her book
• kitap koyuyorum = I am putting a book / books in a more general sense

With possessed nouns like his book, the object is usually specific, so the accusative is very natural and usually expected.

Because masa is receiving the action as a destination.

• masa = table
• masaya = to the table / onto the table

The ending here is the dative: -a / -e.

Since masa ends in a vowel, Turkish inserts a buffer y:

• masa
  • -a → masaya

With koymak (to put/place), Turkish often uses:

• the thing being moved in the accusative
• the destination in the dative

So:

• kitabını = the thing being put
• masaya = where it is being put

Because masada means on the table / at the table as a location, not a destination.

Compare:

• masaya koyuyorum = I am putting it onto the table
• masada duruyor = it is on the table
• masada = at/on the table
• masaya = to/onto the table

So koymak usually wants a destination idea, which is why masaya fits.

It breaks down like this:

• koy- = verb stem, put/place
• -uyor = present continuous marker here
• -um = first person singular, I

So:

• koyuyorum = I am putting

The exact vowel in the -yor form changes according to Turkish sound rules, so here it becomes -uyor.

Usually it matches English I am putting, but not always perfectly.

In many cases, -yor describes an action in progress:

• koyuyorum = I am putting

But depending on context, it can also sometimes express a more general present meaning, similar to English simple present.

In this sentence, though, the most natural reading is the ongoing action: I am putting his/her book on the table.

Because Turkish normally prefers Subject-Object-Verb order.

This sentence follows a very typical Turkish pattern:

• Ben = subject
• onun kitabını = object
• masaya = destination
• koyuyorum = verb

So the overall structure is very natural.

Turkish word order can change for emphasis, but the verb often stays at the end.

For example:

• Ben onun kitabını masaya koyuyorum. = neutral
• Onun kitabını masaya ben koyuyorum. = emphasizes I

It can mean either one.

Turkish does not mark gender in the third person singular the way English does.

So:

• o = he / she / it
• onun = his / her / its

You usually learn the correct English choice from context, not from the Turkish word itself.