What is the ruling on paying off unknown debts owed by her deceased father, and is it permissible to give charity with the intention of settling those debts?

If you know the amount of debts owed by your father but do not know the creditors and are unable to identify them, then you can give the entire amount as charity on their behalf. Estimating an arbitrary amount is not sufficient. Ibn Taymiyyah said: "If a person has in his possession usurped property, borrowed items, deposits, or pledges, and has despaired of knowing their owners, then he should give them as charity on their behalf, or spend them for the benefit of the Muslims, or hand them over to a just distributor who will spend them for the lawful benefits of the Muslims."