Damn! Lucky bugger, it's like the J20 was putting on an airshow display for him.
As for the shaky camerawork, well you can tell at parts that he was sprinting to get the plane back in view when it disappeared behind some houses. I don't think the guy filming it ever planned on it, it was just a case of sheer dumb luck that he was at the right place at the right time, and the shaking is probably largely down to his excitement.
As for the J20's flight, well its hard to judge with all the shaking and moving around, but it looks like some pretty tight turns! At this early stage, I very much doubt that she has been cleared to fly at anywhere close to max G, so the fighter pulling a full 9G turn would be something special to see!
Internet engineer-wannabies can say what they like about it being too long or having too small wings or whatever other such nonsense they can dream up, but when she can fly like that, who cares what those critics think? They more they blab now, the more foolish they will look when the facts come out.