What is the ruling regarding bloodstains from back boils on underwear: Is it sufficient to wash them for purification, or must they be disposed of? And what is incumbent upon one who prayed in clothes without knowing their state of purity?

Blood coming out of boils does not invalidate prayer. A small or large amount of it is excused, and there is no harm in praying with clothes stained with it, provided that it was not caused by your action and that it does not become excessive due to negligence.