Almost. The third person singular possessed ending -(s)i(n) is used to create compound words without using the possessor marking on the initial noun. So:

taksinin şöförü = the driver of the taxi [possessor and possessed marked]

taksi şöförü = taxi driver [only the main noun of the compound phrase marked]

So yes, kitap yazarı is a meaningful phrase. It struck my eye as just a bit strange since I don't normally feel the need to modify yazar but it would certainly have its contexts. I don't think Turkish goes for the compound word quite as often as German, but then, most languages outside of Sanskrit don't.:)

Here you have a Genitive (possessive) construction: Two words are linked with each other

-The owner : gets (n)ln ending - in this case: Kitabın -of the book (no 'n' because kitaP ends with a consonant, ı- for the the 'a' in kitAp (vowel-harmony))

-The possessed: gets s (l) (n) ending - in this case: yazarı -the author (no 's' because yazar ends with a consonant, 'ı' for the the 'a' in yazAr (vowel-harmony) no 'n' -because there is no other case ending (like for instance accusative) to be attached)

Now we have 'the author of the book'.

-'Your book' would be: With the same structure as above 'Sen-İN kitab-İ' -Next step is to glue them together: (sen-İN) kitab-İ + Kitabın yazarı = ? - we drop the pronoun 'senim ' and take only the second part of the term kitab-İ (your book) + (n) because we have another ending following+ the possessive ending (ın) of our second term (Kitabın yazarı)=

Kitabının yazarı - the author of your book.

(I am only a learner, so I hope I got it right)

That's what i thought

"The book's author eats pasta" is correct.

I think you are correct, except it would be kitabı.