What is the ruling on obtaining a loan without usurious interest, which requires a pro forma invoice for household electrical appliances that are not actually purchased, and then using the loan amount for purposes other than those mentioned in the invoice? And what is the solution if that is impermissible?

If the lender stipulates that you must purchase appliances with this loan, or if he only lends to those who need these appliances, then it is not permissible to resort to deception by providing an invoice for another purpose. The loan must be used for the purpose stipulated, in accordance with the Prophet's (peace and blessings be upon him) saying: "Muslims are bound by their conditions."