Is it permissible for the borrower to offer the lender participation in the profits from selling land bought with the borrowed money, or to set a mutually agreeable price for settling the debt and the share of profit if selling is not possible?

What you have proposed, bringing your friend in as a partner with you in the plot of land so that he shares in the profit, and if it cannot be sold, you estimate its value and he takes his share of the profit, is considered an obvious trick to disguise usury. This is the well-known usury of Jahiliyyah (pre-Islamic era), and what is obligatory is to give respite to the one in hardship without increasing the money. It is permissible for you to sell a part of the land to your friend at market price, so that you become partners in it, and you divide its price upon sale. If it cannot be sold, it remains in your ownership. It is not permissible to agree to estimate its price upon difficulty and give him a share of the profit.