I've never signed a child up, so can't answer that part, but good friends with a small child did participate last fall and I've watched the training multiple times.
From what my friend's parents told me, the important things emphasized in the sign up were that the child could understand and follow directions and that the child would be comfortable being away from parents.
What I've seen in the trying is that kids need to be able to follow directions, in terms of going where they are told to go when they are told to go there and to follow certain movements of the light saber or their body. Non-verbal kids should be fine to participate as long as they can do those things.
You can watch YouTube videos of the Jedi training to get a general idea of what to expect. Each show will be a little different, but they follow the same pattern.