Visible crew/equipment: When Kim is talking to Joan the security guard, a crew member drinking a cup of coffee can be seen in the dojo.
Factual error: Jack enters the tournament as a recognized white belt but he is scheduled to face Kim who is ranked as a black belt. Tournaments do not allow match ups between white and black belts; it's forbidden in all styles of martial arts.
Continuity mistake: The ninja with the tattoo that attacks Jack is a large built man with olive skin. When Jack sees the tattoo on Kai's teammate, he is now a slight built, Caucasian teenager.
Continuity mistake: The kids fall to the ground after they are eliminated from the game but when Jerry takes out a knight and the wizard along the path, only the knight is seen lying down in the subsequent shots; the wizard is nowhere to be seen.
Answer: Because he was friends with Kim but he went to the same dojo as the other kids that's how he knows both Kim and the other kids.
No, it never said that. Maybe I'm mistaken, but she wasn't cool with anyone from Bobby Wasabi at the alleged time. So if she did know Carson it wasn't like they were friends, more like enemies if they did know each other.