Aspieparent
In our area we would see your 4 year old and you in our school nurse clinic and work with you on continence and diet, referring to specialist services if necessary. Tn our Trust, once he has a diagnosis, we would fund continence products but also work hard to help him achieve continence if there is no medical reason why he couldn't.
With the eating, he is eating more of a range of foods than some children we work with, although his diet does not seem to be that nutritious, you don't mention if you are worried about his weight or energy levels. As he has seen a dietician, and presumably had bloods done, if they were unhappy they would have prescribed a supplement, but this could also stop his appetite for real food and become a meal replacement, so they are often very reluctant to do this.
With school dinners, we have had this with school in our area and children with additional needs - you could let school try him on the school dinners at first, but also send a packed lunch in so that if he won't have the meal provided by school he will have some lunch. This will also demonstrate to the school that he won't tolerate the school dinners and it's not just you being an over anxious mum. As the school say, sometimes children will eat school dinners if others are, but if he is suspected ASD its not quite that simple. Its worth giving it a try with a packed lunch as back up. He should still be allowed to sit with his peers who are having school dinners, to do otherwise would not be inclusive. Schools have to make reasonable adjustments for children with disabilities, and this would be a very small adjustment for them to make.