Must one make up for a fast if, after the dawn adhan, one burped and drops of milk came out with the burp, reaching the mouth, and were then swallowed by mistake? And what about repeated burping where the taste reaches the lower throat without anything coming out into the mouth?

If something enters the throat by mistake or forgetfulness, the fast is not invalidated, and the fast of one who swallowed something by mistake is valid. However, if a fasting person intentionally swallows something that came out of his stomach into his mouth, while being able to expel it, then he must make up for that day.