Who killed Ali, may God honor his face, and who killed Fatimah?

The man who killed Ali ibn Abi Talib was Abd al-Rahman ibn Muljam al-Himyari, aided by Shabib ibn Najra al-Ashja'i al-Haruri and Wardan. They ambushed him in the mosque, and when he emerged, Shabib struck him, then Ibn Muljam finished him off by striking him on his head, causing his blood to flow, and he died as a martyr. As for Fatimah, may Allah be pleased with her, she died six months after the Prophet, peace and blessings be upon him, and it was also said three months, due to an illness that afflicted her, and no one killed her.