Is it permissible to mortgage an unused agricultural plot or farm belonging to my father, with his consent, in exchange for obtaining financing for building a house from an Islamic bank that deals in Murabaha and requires a mortgage?

If a transaction with an Islamic bank meets the Shariah requirements and is free from prohibitions, then there is no objection to it. There is no objection to the bank stipulating the mortgaging of the land as security for its debt, even if the land is not owned by you, so long as its owner has consented to its mortgage. It is stated in Sharh Mukhtasar Khalil by Al-Kharashi: "It is permissible to mortgage a borrowed item for the purpose of a mortgage – meaning for collateral – based on Malik's saying: 'Whoever borrows an item to mortgage it, this is permissible, and the mortgagee is entitled to sell it if the debtor does not pay what is due from him. The lender then pursues the borrower for what he paid from the price of the item. And in a narration by Yahya ibn Umar, he pursues him for its value.'"