Must one make up the days on which a fasting person swallowed a little blood and bile present in his mouth upon waking due to overwhelming sleep, and must he rinse his mouth and go back to sleep in the future?

Your fast is not invalidated by the presence of blood in your mouth while sleeping, nor by inadvertently swallowing some of it. If you become aware and find blood, spit it out. There is no immediate obligation to rinse your mouth because of it, but rather when you intend to pray or recite the Quran.