Continuity mistake: When Jack is talking to Kim after he defeats the impostor, in one shot you can see the actor who played the impostor appear over Jack's shoulder; he's just standing there watching the rest of the scene.
Continuity mistake: The lockers in the Bobby Wasabi dojo change from blue to green in the same episode.
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.