Is it permissible for a farmer to lease his land, including the crop residues, to shepherds for their sheep after harvesting?

Leasing is valid for usufructs, not for physical entities. The remains of the crop are a specific entity. Leasing a tree to take its fruit, or a sheep to take its milk or wool, is impermissible because it involves intentionally acquiring a physical entity. If the shepherds' aim is to graze on the remnants of the crop or the grasses adjacent to it, then a contract can be made with its owner, but this contract is a sale, not a lease. For the sale of this plant juzāfan (by estimation), certain conditions are required: that it be seen at the time of the contract, that both parties be unaware of its exact quantity, that they estimate it when entering into the contract, that it be neither excessively large nor excessively small, and that individual units not be intended unless their price is low.