Do the rulings on Ramadan fasting apply to voluntary fasting in terms of the permissibility of completing the fast if one eats or drinks out of forgetfulness, and is the supplication of the fasting person before breaking their fast answered, as it is in Ramadan?

There is no difference between one who eats or drinks forgetfully while observing an obligatory fast and one who does so while observing a supererogatory fast, except that the one observing an obligatory fast must complete it, and there is no make-up day required for him. As for the one observing a supererogatory fast, it is recommended for him to complete it, because he is the master of his own will; he may complete his fast if he wishes, or he may break it if he wishes, whether he ate or drank forgetfully or not. The answering of the fasting person's prayer at the time of breaking the fast is general for anyone who is fasting, whether it is an obligatory or a supererogatory fast.