What is the ruling on the transparent discharge that comes out in abundance during ovulation days from a single woman, and is ritual purity (tahara) obligatory from it for prayer?

The secretions mentioned are pure but invalidate wudu'. If their discharge is continuous such that there is no time available for purification and prayer, then your ruling is that of one afflicted by سلس (incontinence). Perform wudu' after the time for prayer has begun, and pray as much as you wish until that time expires.