Does swallowing a hiccup invalidate the fast, and what is the ruling on the prayer of one who involuntarily expels something from the stomach during prostration, and must whatever follows it, be it digestive fluids or vomit, be expelled?

If a fasting person intentionally swallows burps that have substance, their fast is invalidated. However, if it is merely air, it does not affect the fast. The fast is invalidated by intentionally swallowing vomit or stomach acid if they reach the mouth. But if vomiting overwhelms you and you do not intentionally swallow it, your fast is valid. As for a small amount of vomit exiting during prayer without intentionally swallowing it, it does not invalidate the prayer. The questioner should beware of obsessive doubts.