Is it possible to talk to this person and explain how large the trees will get, how they will drop those spiny walnuts on your garden and what the tree roots do?* Maybe they would reconsider their choice or placement?* I can get you sites with all the 'dirt' (pun intended) on these trees if you like.
In the meantime, there are rootbarriers, but you would probably need a pro to install them.* Here you go.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.