Question: When Carson arrives at the dojo he is friends with everyone except for Jack. But Kim didn't know any of the other kids until Jack because she was a black dragon. How did they all know him?
Answer: Kim says Carson taught her to dance, so we can assume they were friends. Even though Kim was a Black Dragon and didn't hang out with the Wasabi kids, she could easily have been friends with Carson since they went to the same school.
Answer: Because Jack came through a wall.
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.