Welcome hathor!
Its definitely possible to be gluten-free and vegan - my family is (I should qualify that - we're strict dietary vegans with the exception of honey)! We never try to eat out!

My son is also corn-free (who would have guessed that xanthan gum and citric acid contain corn?) and has been soy-free until the last couple of weeks when we started him on a soy rotation of every 4th day. He does love his tempeh, tofu, and cinnamon kale stir-fry (which he won't eat without tamari!)!
As for reading recommendations - definitely read The Gluten File! There should be a sticky for it at the top of this forum. Also, look for Kim's post on doing an elimination diet. I have yet to do a proper elimination diet, although I still want to do one... We've always picked a "suspect" food and eliminated it.
Good luck - there's a wealth of information on these boards!