Please check into the Gluten Free Casien Free diet. And other possible food allergies. I have two sons with Autism and after the diet they eat a much wider variety of foods and I found out that they were also allergic to egg, fish, and apples. These are things Iwould have never figured out without the diet and my DAN doctor. Also some vitiams have helped.
From the measurements you stated, your son's weight is in the 50th percentile and height is in the 10th percentile for his age. Suggest speaking with the school and let them know that your son drinks Pedisure, is a picky eater, and is not eating all day. They should allow him to have Pedisure and maybe some other foods after you speak with them. To ‘broaden his tastes’ is to engage him in the kitchen more. Children love to be a part of making food. Have him help you with preparation of food and setting the table. Hopefully this will increase his interest in other types of food.