Ok, so nut and oral allergy syndrome...
I would suggest putting diced or grated vegetables into everything. Meatloaf, sauces, burgers, etc. I'll put a couple recipes at the bottom, you can tweak as needed. Roasting veggies and fruits make them seem sweeter, so kids like them more. Anything mashed is easier for kids, because they can see exactly what it is.
Mash:
1 white potato
1 sweet potato
1-2 parsnips
3-4 carrots
1 turnip
1 rutabaga
Beets (golden and normal)
Boil them in the same pan. Beets go in first, then carrots, parsnips, rutabaga and sweet potato. White potato and turnip go in last. Put all the veggies on a cookie sheet and freeze for about 15 minutes, put about 1/3 of the water in a bowl in the freezer. Blend the veggies, adding just enough of the water to smooth. You can add sour cream, butter, cream cheese or anything else to change the taste. I'm not sure which spices you can do, so not going to say anything there.
Roasted Veg:
1 sweet potato
2 parsnips
carrots
Cut all the vegetables into strips or coins about the same thickness, but leave the lengths/diameters different (different textures once cooked). I toss the raw vegetables with a high heat oil, then sprinkle with spices. Bake until all vegetables are crisp on the outside, tender inside.
Meatloaf
1 lb lean meat, ground (rabbit, chicken, turkey, etc.)
1 lb. fatty meat, ground (15-25% fat pork, beef, sausage, etc.)
3-6 oz spinach, chopped fine
1 onion, diced
2 green onions, diced
1 tomato, diced
1-2 carrots, grated
1 small zucchini/summer squash, grated
4-6 eggs,
1 can tomato paste
1 small can tomato sauce
oatmeal, no more than 1 cup
1 Tbsp high heat oil
Mix meat with your hands in a large mixing bowl and set aside. Whisk eggs, add tomato paste a splash of tomato juice. Mix vegetables and egg mixture into meat with your hands. Sprinkle in oatmeal, but make sure that you still have plenty of moisture, you don't want it to dry out. Meatloaf goes in the pan, remaining tomato sauce mixed with oil poured over the top. Bake on 325 until meat thermometer reads 165.
Pasta sauce
1 can tomato paste
1 small can tomato sauce
1 onion, diced
1-2 green onions, diced
1-3 cloves garlic, minced
1 bell pepper, diced (any color)
1 carrot, grated
1 tomato, diced
1 pear, diced
1 apple, diced
1 lb. meat, ground (10-20% fat works best)
medium heat fat/oil
Saute onion and garlic in fat/oil until onion becomes translucent. Add 1 lb. ground meat, cook until meat is done, drain fat. Add peppers, pear, carrot, cook until peppers are getting soft. Add apple, tomato, green onions, spices, cook for 3-4 minutes. Add tomato paste and tomato sauce, simmer for 5 minutes.
Smoothie:
almond milk, unsweetened
1 banana
1 apple
1 pear
1 peach
1 zucchini
1 carrot
1 small pumpkin or winter squash (acorn, butternut, buttercup, etc)
1 small sweet potato
1 cup Greek yogurt
1 Tbsp low/no heat oil
Roast all veggies and fruits in the skins, squash needs to be halved to roast. Make sure that you roast the banana in the skin or it will be a mess! Freeze extra fruits and veggies for later, cool the fruits and veggies for that day. Blend 1 cup Greek yogurt, portions of each fruit and vegetable together, add oil and almond milk to smooth. If you can do spinach and cucumber raw, you can add 2 oz spinach and a but of cucumber too. A drizzle of honey can sweeten it, but with roasted fruits and veggies, you should be fine.
Oatmeal:
oatmeal
almond milk
peanut or almond butter (if your son can have it)
canned pumpkin
1 egg
hard fruit, diced (apple or pear)
soft/medium fruit, diced (peach, nectarine, plum, cherry)
small berries, whole OR strawberries, diced
grated carrot
grated sweet potato
Mix pumpkin, egg and a splash of almond milk in a bowl. Heat almond milk in a pan, add grated carrot, sweet potato, hard fruit and cook until semi-soft. Add all other fruit, cook 2 minutes. Add nut butter (if possible) and sift in oatmeal, stirring constantly. Make sure that you add only 1/3-1/2 as much oatmeal as liquid/fluid in the pan. Cook for 4 minutes, then stir in pumpkin mixture, cooking for a few minutes. Do not overcook, but you need to make sure the egg is completely cooked.
Oils:
high heat: almond, avocado, grapeseed (preferred), safflower, refined sesame, sunflower
medium heat: butter, unrefined coconut, ghee, walnut, macadamia (prefer butter, coconut or walnut, depending on recipe)
no/low heat: extra virgin olive oil (preferred), unrefined sesame, pumpkin seed
Fiber can help constipation, but fats and water help as well. Make sure that he has enough of all three, and it should be easier to keep him from having issues.
Sorry, I know that the recipes are for larger families, you could try to scale them down.