Is Zakat obligatory on a sum of money designated for a medical procedure that was postponed and decreased before the passing of a whole year? And if it is obligatory, is Zakat to be paid on the original amount or the remaining amount?

What remains of the saved money is subject to zakat (definition) if a full year (hawl) has passed on it while it reaches the nisab (definition). As for what has been spent from it, there is no zakat on it. The nisab for banknotes is equivalent to 85 grams of gold or 595 grams of silver, and the amount of zakat to be paid is a quarter of a tenth (2.5%).