Is it permissible to deduct the remaining price of the apartment—which has not yet been delivered and its installments have not been paid—from the money upon which a year has passed and zakat is due, and then pay zakat on the remainder? And does the ruling differ if the delay in delivery was due to me?

As long as you are indebted, there is no Zakat (definition) due on the aforementioned amount if the debt reduces the saved money below the nisab (definition), and you do not possess other money exceeding your basic needs. However, if you do have money exceeding your basic needs, use it to offset the debt and then pay Zakat on the remaining Zakatable money. Receiving the apartment has no effect on the Zakat, because the debt remains binding upon you.