Am I obligated to make up a day of fasting if I am uncertain whether a year has passed since it was missed, and is it permissible for me to be cautious by feeding a needy person even if I do not possess the money, and is it permissible for my father to pay it on my behalf, and must the food be cooked?

Whoever was ignorant of the obligation of the fidyah is not bound by it. And whoever doubts the time of breaking their fast should attribute it to the nearest time, and the fidyah is not obligatory upon them. The required amount for feeding, according to the majority of scholars, is giving ownership to a poor person of half a saa‘ (1.5 kilograms) according to the Hanbalis, and half of this amount (750 grams) according to the Shafi‘is and Malikis. And whoever is unable to pay the expiation, it remains a debt upon them until they are able to.