Verified answer

książki is in the Genitive because you're using the verb uzywac.

However, the clause którą mi dałaś uses the verb dac, which takes the Accusative in the affirmative sense. So it ktory takes the feminine Accusative (not Instrumental) here.

That's how który and its cognates in other Slavic languages generally work. It's a case switcher that only carries the gender and number. In this case, it's the feminine singular that connects the relative pronoun with "książka" in the previous clause.

Simply put, same reason that you say "of the book that you gave me" and not "of the book of which you gave me".

When you want to preserve the case, you use participles. So in this case (theoretically, as this probably sounds very unnatural) you'd go "używam książki, danej mi od ciebie" ("of the book given to me by you"). Like I said, it sounds awkward, but there are other occasions when it's better to use the participle rather than the relative pronoun.

Edit: @Ame, it absolutely should be in the accusative. To give you the benefit of the doubt, you're probably mixing it up with the negational genitive of "której mi nie dałaś".

Yes, this is correct, because the verb używać can only be used with genitive (używać kogoś/czegoś), but I don't know who told you that który should be in accusative here, it does not make any sense, it should be in genitive:

Używam książki, której mi dałaś (if it's a she) / dałeś (if it's a he).