Do doubts affect the intention for an obligatory prayer, or the intention for making up missed fasts followed by six days of Shawwal, or does remembering food and wishing to break the fast affect the validity of the fast?

The worshipper should not surrender to doubts and whisperings. If he says the takbir intending a fard (obligatory) prayer, he should proceed with his prayer according to his intention and not pay attention to the doubts cast by Satan that he might be praying another prayer or that his intention has shifted to nafl (supererogatory). Similarly, whoever intends to fast a qada' (make-up) fast is bound by his intention, so he should proceed with his fast and not pay attention to the doubts that come to him that he wants to fast a nafl. Remembering or seeing food and desiring it does not invalidate the fast. If the worshipper were to indulge in such whisperings, they would corrupt his religious and worldly life.