Is it true what is narrated about Fatimah or A'ishah (may Allah be pleased with them both) being bewitched by a Jewish woman, and that the spell was broken when a small animal burst in the fire unintentionally? And is it permissible to use this animal to break spells?

The one who was bewitched was the Mother of Believers, Hafsa bint Umar ibn al-Khattab. She was bewitched by one of her slave girls, so Hafsa killed her. Uthman disapproved of her action. As for the method of breaking magic mentioned in the question, it is deception and charlatanism, due to its contradiction with Islamic law, especially the burning of an animal with fire.