What is the ruling on someone who vomited before the Adhan, then drank and smoked after the Adhan, claiming thirst, while knowing the prohibition of violating the fast? And is he only required to make up one day?

The presence of a burning sensation or thirst does not permit breaking the fast. Therefore, a man consuming things that break the fast after the Fajr adhan (definition) is a mistake that necessitates repentance and making up the fast, along with abstaining for the rest of the day. His statement that he did not intend to violate the sanctity of the month does not excuse him. He must also quit smoking due to its impermissibility.