Is an expiatory oath (kaffarat yamin) obligatory upon someone who vowed to fast for a full consecutive year if certain conditions were met, and some but not all of these conditions were fulfilled, while being unable to feed or clothe [the poor]? And would the expiation be due after fulfilling the vow? And is it permissible to complete the vowed fasting after Ramadan, the six [days of Shawwal], and making up any missed days?

The Prophet, peace and blessings be upon him, forbade vows because they do not avert anything and are a means to extract from the miserly. If a Muslim vows an act of obedience to Allah contingent on a condition, it becomes obligatory to fulfill it when the condition is met. If the total score did not qualify for entry into the desired college, then the condition of the vow has not been met, and nothing is binding. However, if the total score did qualify for entry, but you chose not to enroll, then fulfilling the vow becomes obligatory. The fulfillment of a vow contingent on a condition must be immediate. If one vows to fast for a consecutive year, Ramadan, the two Eid days, and the days of Tashreeq are not included in the vow, and there is no need to make up for them. Menstrual days do not break the continuity, but they must be made up. However, making up for Ramadan and the six days of Shawwal do break the continuity, which is why the vow takes precedence over them. If the time for making up Ramadan fasts is limited, you should fast the make-up days first, and then complete your vow.