You misunderstand me. I don't mean he's small because of malnutrition. And I certainly don't mean they're not feeding him. I mean that whatever underlying condition he has is also screwing up his ability to tolerate nutrition. And you absolutely have to be able to get enough calories in for the GH to work. Even if he is GH deficient, and even if GH is part of the right treatment, if they don't find a way for him to cope with enough calories to grow it won't get anywhere.
But diagnosing him would require:
A very detailed history
A decent examination
Developmental assessment
Extensive xrays
A variety of scans
Lots of bloods, urine samples etc for metabolic, endocrine, and genetic disorders
Input by at least a geneticist, a paediatric endocrinologist, a paediatric gastroenterologist, a paediatric orthopaedic doctor, a paediatric radiologist, a really good paediatric dietician. And quite probably also paediatric surgery, and maybe spinal surgery and cardiothoracics.
In the UK, he wouldn't just be at a children's hospital (ie local DGH would not be able to work this out), but probably at least being discussed by them with GOS.
I'm afraid the odds of us being able to actually help over the internet is pretty minimal, because (as the GMC would put it) we cannot put ourselves in the position to properly assess the patient. With a 3rd hand history, no examination, and no results. Hence going back to the basics of any intervention made to try to promote growth has to include sorting out calorie intake, as that is true for any cause.