Learn Farsi: این کتاب بسیار خوب است.

Both kheyli and بسیار (besyaar) mean "very" or "a lot." The word بسیار is slightly more formal, literary, or emphatic. You will see it often in writing, whereas خیلی (kheyli) is the most common word for "very" in everyday spoken Farsi. You can generally swap them without changing the core meaning.

Does the adverb of degree (besyaar) always go right before the adjective (khoob)?

Yes! Just like in English where "very" sits right in front of "good," Farsi places the adverb of degree (بسیار) directly before the adjective (خوب) that it makes stronger.

If I wanted to say "These books are very good", would the word for "this" (in) change to become plural?

No, it wouldn't change at all! In Farsi, demonstrative words like این (in, meaning "this") do not change to match plural nouns. You would just make the noun plural (کتاب‌ها / ketab-ha) and leave این exactly as it is.

How would a native speaker actually say this sentence in a casual, everyday conversation?

In relaxed spoken Farsi, the formal "is" verb است (ast) is almost always shortened to an "-e" sound attached to the previous word. A native speaker would most likely say این کتاب بسیار خوبه ().