Is it permissible to deduct what was paid from the father's debt during his lifetime from his estate after his death, or does that fall under "You and your wealth belong to your father" and thus is not to be deducted from the estate?

If you paid the money to settle your father's debt with the intention of recovering it, then it is a debt owed to you by him, and you have the right to take it from the inheritance before its distribution, like any other debt. However, if you donated it without the intention of recovery, then you are only entitled to your lawful share of the inheritance.