How can the unknown amount and parties of a deceased person's debts be settled?

A person is only obligated by what they know. Therefore, any debts of your father that you were unaware of are considered non-existent by ruling. If you paid off the debts of the deceased that you knew about, and then other debts emerged, the heirs must pay them from the estate according to their shares, or the distribution should be revoked, the debt paid, and then the remainder distributed. As for an interest-bearing loan (riba), only the principal amount needs to be repaid. You can announce the death and request anyone who has a claim to a debt to provide proof.