In this paper, we investigate the effects of residual hardware impairments (RHIs), channels estimation errors (CEEs) and imperfect successive interference cancellation (ipSIC) on the cooperative non-orthogonal multiple access (NOMA) system over Nakagami-$m$ channels, where the amplify-and-forward (AF) relay can harvest energy from the source. The exact expressions for outage probability and ergodic sum rate are derived in closed-form. In addition, the asymptotic outage analyses in the high signal-to-noise (SNR) regime are carried out. The results show that the outage probability exists an error floor due to the existence of CEEs and compared with RHIs, CEEs have a more serious impact on the system outage performance. The close simulation results of Monte Carlo verify the accuracy of our theoretical derivation. Finally, the performance of energy efficiency is examined with RHIs, CEEs and ipSIC.