Is zakat immediately due on newly acquired wealth that has not yet completed a hawl (a full lunar year), or can its zakat be postponed until next year? And was it a mistake to postpone the zakat on the wealth added from last year, necessitating rectification?

If the new money is generated from the original money that has reached the nisab (definition), then zakat (definition) is paid on it along with the original money at the same time, even if a year has not passed over it. However, if it is not generated from it, then it has its own independent year.