How much of the diagnosis and traits should I tell the lesson instructor?

You don't have to tell everything, but sharing information useful for safety and for the child enjoying and continuing brings reassurance. Rather than the diagnosis name itself, conveying concrete ways of relating—"this situation is hard," "it's clearer if you say it this way," "this calms them"—makes it easier for the instructor to respond. Summarizing it briefly, like a support book, is handy. What to tell is decided respecting the child's age and wishes too.