The two at the end of each Katya Strom video are Hyunjin and Felix, it's taken from a live stream they did together. Then the "thank you for coming etc..." is from one of Hyunjin's live dance practises
Baby Girl when referring to a guy is when they show a lot of aegyo in efforts of getting taken care of or getting others to do their bidding or flat out wanting extra attention. That is how it's being used that I've been seeing anyway