How is the Zakat calculated for a driving school, and is it estimated based on the value of cars and furniture as capital, or based only on profits (2.5%)? And how is Zakat paid for past years for which it was not paid?

What you use in school, such as fixed assets and presentations not intended for trade, is not subject to zakat, because they are acquired for their produce, and because zakat is not obligatory on commodities unless they are intended for trade, by consensus.

Zakat is obligatory on the money you acquire from this school if it reaches the nisab and a full Hijri year has passed over it.

If zakat became obligatory upon you in past years and you did not pay it, you must repent and hasten to pay it, for it is a debt upon you that cannot be absolved except by its fulfillment, according to the hadith: "The debt owed to Allah is more deserving of being paid." If it is difficult to ascertain its exact amount, then pay what you believe with strong conviction will clear your liability.