Whether the Testimonium Flavianumin (Josephus’ description of Jesus in Antiquities) was entirely a Christian insert or the section was just edited by Christians is debated, however there’s consensus that Josephus’ reference to “the brother of Jesus, who was called Christ, whose name was James” in Antiquities is authentic.
Cougars absolutely can and do eat cats and dogs; their natural prey is primarily deer but they’ll absolutely hunt smaller animals if given the opportunity. It’s also not unheard of for them to stalk children and even adults.