Is it permissible for a teacher to lend money to a farmer, knowing that the farmer is unable to sell his crops to anyone else, and without an explicit condition, provided that the teacher demands only his money back without any increase if the farmer sells his crops to someone else?

It is not permissible to give a loan on condition that the borrower sells something to the lender, because every condition that draws a benefit to the lender is usury (riba). This includes tacit agreement for benefit. The Prophet, peace and blessings be upon him, forbade "a sale and a loan together," and the Companions forbade any loan that brings a benefit. It is permissible to return something better than the loan if it is without a condition or tacit agreement. However, if it is customary to give crops to the lender in return for the loan, this is considered a condition and is not permissible.