Is a doctor's reduction of the examination and laboratory test fees to half price and giving charity to the poor considered a form of zakat on wealth? And if not, what is the ruling regarding previous years in which the annual zakat was not paid?

Providing for the poor and waiving or reducing their rent are acts of worship for which the doer is rewarded, but they are not considered zakat. Among the conditions for the validity of zakat are the intention at the time of payment, and giving to the poor and transferring ownership to them, as stated in the Almighty's saying: (Take from their wealth a charity by which you purify them and cause them increase). What occurred was merely a waiver of rent, not a giving, therefore it is not valid to consider it zakat. Zakat must be paid for previous years by estimating the wealth in each year.