My daughter also cannot eat cheese, nor soy, so finding a good cheese substitute was challenge. Fortunately, we succeeded in finding a great one. It's called "Daiya" brand. It's available at health food stores including Whole Foods. It melts and pulls like cheese and has a great taste. 

 

Eggs are easier: The best product is called "Egg Replacer" by Ener-G Foods Inc. It's available in all health food stores in the baking section, as well as in many regular supermarkets.  It comes in a box, like a cake mix, and you use something like one tablespoon with a little water per egg.  Directions are on the box.  Works great.

 

There are actually a number of other egg replacers that work very well depending on what you're cooking.  Tofu, for example, works very well where a lot of eggs are involved, like in quiches, or even tofu omlettes! 

 

Flax seeds also work, as well as various vegetable oils.  I suggest you do a quick Google search on "Egg Replacers" and you'll find recipes for exactly what you're doing.  In the meantime, here are some others that work:

 

2 tbsp corn starch = 1 egg

2 tbsp arrowroot flour = 1 egg

2 tbsp potato starch = 1 egg

1 heaping tbsp soy powder + 2 tbsp water = 1 egg

1 tbsp soy milk powder + 1 tbsp cornstarch + 2 tbsp water = 1 egg.

1 banana = 1 egg in cakes.

 

Enjoy in good health!

 

Missy