Acccording to LoShmidt's Number does that mean every atom occupies the same volume in a structured material?

Answer 1

No, for two reasons. First, it applies only to an ideal gas. Second, it says nothing about the volume occupied by a single molecule (not atom), but instead by a gas composed of many molecules in motion. It says nothing about a 'structured material', by which I assume you mean a crystal, Buckminsterfullerene, or related material.