What is the ruling on making up missed fasting days when their number has been forgotten, and is it permissible to offer a fidyah (expiatory payment) along with the fasting? And can the fidyah be paid all at once to a single poor person?

We understand from your question that you are fasting with the intention of making up for six days for each past year in which you did not make up the days you owed. Therefore:

1. It is not permissible to postpone making up the fast over several years if one is able to hasten it. 2. If you do not know the exact number of days you owe, then make an effort and fast what you are certain of, or what you predominantly believe, will clear your conscience. 3. In addition to making up the fast, you are required to pay a fidyah (expiatory feeding) for each day you delayed making it up without a valid excuse until the next Ramadan began. The amount is feeding one needy person (approximately 750 grams of rice). 4. The fidyah is not repeated for delaying the make-up fast for several Ramadans, and it is waived if the delay was due to ignorance or forgetfulness. 5. There is no objection to giving the fidyah before, after, or during the make-up fast. 6. The principle for fidyah is that it should be given as food, not money, and most scholars do not permit giving it as money. 7. There is no objection to giving the food to a single needy person.