Is Zakat due on the entire inherited olive harvest, or on half of it after paying the wages of the person responsible for its care and collection? And are the necessary care expenses deducted from the Zakat value?

If the contract with the one who harvests the fruit is a musaqat contract (sharecropping for orchards) and he has a known share of the produce, then zakat is obligatory on each person for his share if it reaches the nisab. However, if the contract is one of ijarah (leasing/renting) and all the produce is owned by you, then zakat is obligatory on you if it reaches the nisab, which is five awsuq. It is not permissible to deduct what you spent on caring for the fruits or working on them from the zakat.