I would  love to hit the like button on your post, space.

Totally vegan here, with allergies to a long list of foods including peanuts and tree nuts, but coconut is ok.  We eat plenty of seeds (from Libre Naturals, Gerbs, or Sunbutter), fruits, vegetables, quinoa, rice, oats, tofu, etc.  Pretty much everything we eat is whole foods and fresh. 

I haven't found a completely tree nut-free milk alternative other than tinned coconut milk, but we generally only use it for baking and ice cream.  As for cheese, Daiya is a vegan substitute that isn't nut-based and many people like it, but it is heavily processed. 

I would suggest you start with a good vegan cookbook like Eat Clean Live Well, Veganomicon, or Vive le Vegan and see if you like those recipes and feel like they would sustain you.  Chocolate Covered Katie (website and book) also has some incredible recipes that we love to pieces.  I'm very athletic and find the vegan diet works well for me, but it doesn't sustain everyone. 

I'm allergic to peanuts, tree nuts, mango, banana, kiwi and avocado. I know a lot of cheeses are made from cashews, etc with vegan diets.  Has anyone successfully went vegan with allergies?