The planes aren’t actually planes but really thin squares. Even one-sided, I should at least see the texture from one side. Every self made model (convertet to .fbx by blender) has the problem. Downloaded meshes work fine. I actually don’t know what you mean with UV unwrap, I’ll get into it when I’m back from work! Thanks for the idea.
Without UV unwrapping, the image doesn’t have a clue about how it should be placed on your plane (or your box).
If you look at the first image you posted, it’s nothing but this mossy green color. Perhaps you’re only seeing 2 tiny pixels from your actual image. I can’t say this more detailed than the lien above; your image simply doesn’t know where it should be placed on your plane/box, or even how big/small it should be.
Other than that, you should make them two-sided so the leafs will be seen from both sides of the plane/box