I'll be rather brief, maybe you have follow-up questions after that.
Yes, we always use periodic boundary conditions in MD, although you can of course have vacuum around a structure like a CNT etc; since the range of interatomic forces in classical potentials is usually quite short (electrostatic forces may have longer range) this effectively makes the system 1D.
For devices, however, since the electrodes and their repetitions (more correctly, the electrode extension) are indeed always fixed, it's sort of not periodic in Z, since the atoms cannot move there. Not sure what you observe about atoms leaving the cell, you'd have to show an example.
Cell size will change if you are using NPT, but I would use the device structure, because a small change in atoms doesn't make a difference, at least for forcefields. For DFT, you would have to think carefully about doing an MD simulation for such a large structure as a device. Keeping it as a device structure makes it much easier to do a DFT-NEGF calculation afterwards, without worrying about the cell size change or atoms in the electrode extensions moving.
Do not repeat in Z if it's a device, but otherwise yes, you usually need a relatively large supercell, else you are limiting the degrees of freedom the systems can explore.