Is the mentioned calculation for gold zakat correct, and how is the zakat calculated for previous years that was paid in installments, and are there any scholars who deem it permissible to pay delayed zakat in installments throughout the year?

The calculation mentioned is correct in terms of the mathematical equation and the Shar'i (Islamic legal) consideration. However, paying Zakat based on the Gregorian calendar and in installments is an error that necessitates repentance and not reverting to it. Nevertheless, the Zakat paid is sufficient, and there is no need to pay it again for past years if the full Zakat was paid in each year (Hawl).