And what was that thing about baby Jesus (PBUH) talking to people and telling them that he's a Prophet about? Is it documented that it was like that anywhere? Any Islamic sources?
Yep its true. Prophet Isa(as) did testify
" She made a sign to them, pointing to the child. But they replied : 'How can we speak with a baby in the cradle?' Whereupon he spoke and said : I am the Servant of God" (19:29-30, Koran)