“BoJack, you are amazing! You're bright, and you're funny, and you're handsome, and you're talented. If you can't see that, then you're the biggest, dumbest, piece of shit in the world.”

The baby was Ani and Ray's. In the previous scene where Ani is talking to the reporter she mentions "his sons" plural.

I assumed "the kids" meant the other members of F-Society.

Lloyd (fat glasses guy) was in the room sitting near the door. They had the camera on Mr Robot when Romero said the line so we don't know who he was talking to.