Are the prophets infallible, and if so, how is what happened to the Prophet Jonah (peace be upon him) explained?

The Prophets are infallible in conveying messages from Allah, and in not committing major sins or minor sins that indicate baseness. As for minor sins that do not indicate baseness, they may commit them, but they are not left to persist in them. Rather, Allah Almighty intervenes and alerts them, so they repent from them. After repentance, they attain a higher status than they had before, for what matters is the perfection of the end, not what happened at the beginning. The stories of Adam and Yunus, peace be upon them, are evidence of this.