"эту книгу" changes the last letters of both words because the verb acts on "this book"?
Right! «Э́ту кни́гу» is the accusative case, used for objects. «Э́та кни́га» is the nominative case form, used for subjects.
That extra DO would emphasize the sentence, like if someone was accusing you of not knowing it.
Would this mean that the book is familiar to me (I've heard about it), I am familiar with a specifix book (I see a book that I lost three years ago and on a bus, I happen too see it and exclaim that "I know that book!" Or woukd this mean that I have memorized all of the knowledge in the book in question?
that's because это can function as "The" in some occasions (even when there is no equivalent to the word in Russian), but always equivalent to "This".
*I'm not native speaker, but I've read this explanation before :)