Breakdown of Sie brauchen Ihren Leseausweis für die Rückgabe.
Sie
you (formal)
brauchen
to need
Ihr
your (formal)
für
for
Questions & Answers about Sie brauchen Ihren Leseausweis für die Rückgabe.
Where would I insert gefälligst into this sentence if I wanted to make a very angry demand?
You would generally place it right after the verb: Sie brauchen gefälligst Ihren Leseausweis für die Rückgabe. This instantly changes the tone from a neutral administrative rule to a highly annoyed reprimand, similar to saying "You damn well need your library card..." in English.
Why is the possessive pronoun Ihren used here instead of just Ihr?
As a quick refresher: the verb brauchen requires a direct object in the accusative case. Because der Ausweis (and therefore the compound der Leseausweis) is a masculine noun, the formal possessive pronoun Ihr must take the masculine accusative ending -en.
Is there a difference between a Leseausweis and a Bibliotheksausweis?
They mean exactly the same thing and can be used interchangeably. Leseausweis (literally "reading ID") is just a slightly shorter, very common everyday alternative for a library card.
How is the noun die Rückgabe formed? Is this a common pattern?