Food allergies in children

My daughter was recently diagnosed with a cashew allergy serious
enough to warrant walking around with EpiPens for the foreseeable future. The allergist recommended no tree nuts at all (though she is not allergic to others, he wants to have an easy-to-understand rule since she is just 3).

My main questions are:

1. How do you avoid becoming totally neurotic and overprotective?
2. What sort of things do you do to help your child maintain a sense of normalcy and not feel like an oddball at parties, etc.?
3. Have there been foods that you never thought to contain allergens (in our case tree nuts) that subsequently induced a reaction?

Thanks so much!