What should a woman do if she vowed to spend an entire night in prayer and reading Qur'an, and her vow was fulfilled, but she experiences intermittent vaginal discharge ("rutubat al-farj") during prayer?

The vow must be fulfilled if the condition upon which it was made is met. Vaginal discharge is considered pure according to the preponderant opinion, but it nullifies ablution (Wudu'). If you are afflicted with continuous vaginal discharge, your ruling is that of a person with incontinence. You should perform ablution after the entry of the 'Isha prayer time and pray with this ablution the obligatory prayer and whatever supererogatory prayers you wish until that time expires. What issues forth from you of this discharge will not harm you.