Error performance is considered as one of the most important performance measures, and deriving the closed-form expressions for efficient modulation techniques over generalized fading channels is important for future cellular systems. In this paper, the performance of a dual-hop amplify-and-forward multi-relay system with best relay selection is analyzed over independent and non-identically distributed (i.n.i.d.) Nakagami-m fading links with both integer and non-integer fading parameters. The impact of practical constraints of imperfect channel state information (CSI) and non-linear power amplifier (NLPA) at each of the relays are considered. Closed-form expressions for the outage probability are derived for both integer and non-integer fading parameters, and asymptotic analysis on the outage probability is performed to obtain the diversity order of the considered multi-relay system. Based on the cumulative distribution function approach, average symbol error rate (ASER) expressions for general order hexagonal QAM, general order rectangular QAM, and 32-cross QAM schemes are also derived. The comparative analysis of ASER for various QAM schemes with different constellations is also illustrated. Furthermore, the impact of the number of relays, fading parameter, channel estimation error, and non-linear distortion on the system performance is also highlighted. Finally, the derived analytical results are validated through Monte-Carlo simulations.