Other mistake: They say that when Jack is back, they will be in college, but they were in Year 8 and all 14, so they would be, at most, in Year 12.
Other mistake: They act as if Carson was part of the dojo with the whole crew, but Kim was a Black Dragon when the show started.
Answer: It depends. If you watch the action scenes in slow motion, you can often tell if it's the actor or a stunt double. Leo Howard seems to do a lot of his own fight scenes and acrobatics while many of the fights and flips by other characters are done by doubles; although occasionally Olivia Holt will perform a simple flip or fight.
Both Leo Howard and Olivia Holt have black belts and completed their own stunts.