Is it obligatory to pay the debt a third time, and is the amount doubled, after it was mistakenly given to an impermissible party, following its initial mistaken disbursement as well?

According to the view that holds the expiatory feeding (fidyah (definition)) to be obligatory for delaying the making up of fasts without a valid excuse, your liability and that of your friend have not been discharged. The fidyah is to feed one poor person for each day of delay. The amount of food for feeding is one mudd of food (approximately 750 grams), and it is more cautious to give half a saa' (approximately 1.5 kilograms). According to the majority of scholars, it is not permissible to give the fidyah in cash or as gifts, nor is it permissible to give it to an orphan who is not in need. Therefore, you must re-issue the fidyah in food, in the mentioned quantity, and give it to a poor person.