Is it true that the hen was cursed by the Messenger of Allah, may Allah bless him and grant him peace, and if so, why?

No hadith has been found regarding this matter, and it is not believed to be authentic. The Prophet, peace and blessings be upon him, was not a curser and forbade cursing animals, finding fault with those who did so. He said: "It is not befitting for a truthful person to be a curser," and when a woman cursed her she-camel, he said: "Take what is on it and leave it, for it is cursed."