What about a woman who fasted, prayed, and recited the Qur'an after her menstrual bleeding stopped, then later saw a small amount of blood? Should she break her fast or continue it, and are her prayers and recitation of the Qur'an valid?

Your prayer and recitation of the Quran are valid as long as you believe you are pure. As for the day you saw blood after praying, you must make up for it because your fast was invalidated by the return of menstruation. If no blood descended for two days after seeing the returning blood, you are still considered to be menstruating until you see purity by one of its two signs (dryness or the white discharge). If the two days were before seeing the returning blood and you ascertained purity, then your fast is valid and you are not required to make it up. However, if you did not ascertain purity before seeing the returning blood, then you must make up for those two days. A menstruating woman is permitted to recite the Quran without touching the Mushaf.