You are misinformed. There is no such condition. Just think how much work validating that would be!
In reality there needs to be a statement in the patent from the inventor that the product works, or could work.
No, not true. It does not have to be at industrial level or even something that is profitable. It just has to be useful for someone.
The patent laws require that an invention must be novel, non obvious and useful (if you are in the United States) or be susceptible of industrial application (if you are in Europe; industrial application means that the invention can be made or used in some kind of industry). As far as I know, IH tried to extend their US application even in Europe, where the requirement of industrial application is valid.