Nuclear magnetic resonance (NMR) measurements have been performed on the heavily Cu-doped ($x = 0.13$, 0.18, 0.24, 0.39, 0.48), and underdoped (x = 0.01 and 0.012) \NaFeCuAs~ single crystals, to reveal the nature of the magnetism, and to investigate how the electronic and magnetic properties of the system evolves with...