Which babies are considered hidden? What does it even mean?

Best bet is babies unlocked via achievements

Or if you're talking about the "completing the game with only ??? babies" achievement, you just have to pick the third unknown baby option after completing a level everytime, all the way until you beat chapter 3

The hidden baby's are the ones that are ??? (In case you ask for the item that reveals it or the achievement)

yeah hidden babies are just the 3rd (4th if you have more options) baby pick, the one that's "hidden" with ???, so for the unlock you just have to beat a run while always picking the unknown baby option, i'm not sure if getting crystal ball prevents you from getting the unlock or not

crystal ball does prevent you from getting the unlock