Is it obligatory to estimate and pay Zakat for previous periods after becoming aware of the incorrectness of a fatwa permitting non-payment for a young man about to get married, or is it sufficient to pay Zakat only on current wealth?

Zakat must be given immediately once its conditions of obligation are met. Zakat does not lapse with the passage of time. Zakat for previous years must be paid, and voluntary charity given without the intention of Zakat does not fulfill its obligation.