When should an unmarried girl consider herself pure and perform ghusl, especially when she sees light yellowish discharge tending towards white after her menstrual days? And is what she sees considered istihadah (non-menstrual vaginal bleeding) or a new menstruation that necessitates abstaining from prayer?

If the yellowish discharge continues for most of the month, it is considered istihadah (non-menstrual vaginal bleeding) unless it ceases on the fifteenth day. You should consider the days of blood as menstruation, and any yellowish discharge beyond that as istihadah. After the days of bleeding have ended, perform ghusl (ritual bath), pray, and do what a woman experiencing istihadah does.