Translation:This book is long.
です = polite version of だ = to be
長い(ながい) = long, works like a verb in Japanese ("to be long")
Since ながい already states something is long, you don't need it at all, grammar-wise, but it's considered very polite to add the です in any case!
With these kind of polite sentences, only conjugate the necessary part, not the added です! (e.g. 「この本は長かったです。」 = "This book was long." / 「この本は長かったでした。」 = バカ外人(=goofy foreigner) stuff
No, if you were to have a "na" at the end of a sentence, it would be "da". "Na" is just the connective form of "da": what you would say if you were putting another noun after it. If you were to say that the flower was pretty, you would say, "Hana ga kirei da." But if you were to put the word for "flower" at the end, you would change the "da" to "na": "the pretty flower" would be "kirei na hana".
And in any case, you only do that for so-called "na" adjectives, and "nagai" is not one of those.
So-called "i" adjectives have the "da" or "desu" built into them, so to speak, so you don't need to put "da" or "desu" after them, grammatically speaking: "Kono hon wa nagai," would be a complete sentence without anything after the "nagai".
You can say "desu" after it to make it more formal, but grammatically, you don't need to.
Japanese Adjectives i and na - secrets they never tell you! Four facts that make adjectives easy
21,067 views•Dec 9, 2017
Organic Japanese with Cure Dolly
Literally, as I understand it, it means "to be equal to, to be the same as". It's translated with "to be", because in the end the meaning is the same, but it's not actually the verb "to be". It's more like the = sign.
私は学生です -> "myself = student" -> Regarding myself, I'm equal to a student, I'm exactly the same as a student. Translated: I'm a student.
You're absolutely right!
When you need to be very polite to someone, say talking to your boss or school director for example, definitely add the extra です!
On the other hand, in casual conversations, such as when you're talking among friends, you don't even need to put necessary です's! (e.g. 「あ、、、バカ外人は！」 = "Ah... Goofy foreigner", incorrect Japanese, though it's understood to be "Ah... I'm such a goofy foreigner" after making your so manieth grammar blunder totally not out of experience nah... )
Also, kudos for Rem, Emilia best girl though.