Is it obligatory to re-fast two consecutive months and perform them as a make-up for a vow to join the Faculty of Medicine, and what is the ruling on this vow if the idea of a private university was not proposed at the time of the first vow?

A vow conditioned on an undesirable matter is disliked and brings no good, for it repels nothing, and only what Allah has decreed will occur. A vow is like an oath, and its basis is intention. What is considered in it is the intention. If the intention was to enter a government medical college based on the coordination results, then the condition has not been met, and nothing is binding. However, if the intention was to enter any medical college, then the vow has been fulfilled and it is obligatory to honor it. If there was no intention, one refers to the reason for the vow. If the hope was that the coordination would lead to entering a government medical college, then the vow has not been fulfilled. If the aim was merely to enter a medical college, then the condition has been fulfilled and it is obligatory to honor it. If there is neither an intention nor a reason, the wording is acted upon. Since a medical college was entered, honoring the vow becomes obligatory. As for night prayer (Qiyam al-Layl), it is achieved by two rak'ahs. Therefore, whoever vowed to perform Qiyam al-Layl, fulfills the vow by praying two rak'ahs.