Es comes from ser, and está comes from estar.
Here, es is used because delgado describes a characteristic of the book: its thickness. That is treated as an inherent quality, not a temporary condition.
So:
For a book, está delgado would sound wrong or very unnatural.
Because adjectives in Spanish usually agree with the noun they describe.
Since libro is:
the adjective must also be:
So we use delgado.
Other forms would be:
Very often, yes.
When an adjective directly describes a noun, it usually comes after it:
In your sentence, the adjective comes after the verb es:
That is completely normal.
Putting delgado before libro would be unusual here and would sound literary or marked rather than neutral.