In this paper, we investigate the performance of a hybrid receiver-based simultaneous wireless information and power transfer (SWIPT) two-way relay network over Nakagami-m faded channels. A hybrid receiver is adopted at the relay node that utilizes both the time switching (TS) and power splitting (PS) protocols for energy harvesting and information transmission. Amplify-and-forward relaying protocol is utilized at the relay node to process the information in half-duplex mode. In the considered network, impact of a practical non-linear power amplifier (NLPA) at the relay node is considered. Selection combining is performed at the destination node to utilize the direct-link and relay assisted signals. For the considered system, the analytical expressions of outage probability (OP) and asymptotic OP are derived over Nakagami-m faded channels for both the integer and non-integer value of m. The diversity order of the system is obtained with the help of asymptotic OP. The analytical expression of the system throughput and energy efficiency of the considered network are also derived. Further, the analytical expression of ergodic capacity is derived in terms of the Meijer-G function. By utilizing a cumulative distribution function based approach, analytical expressions of average symbol error rate (ASER) for general order hexagonal quadrature amplitude modulation (QAM), general order rectangular QAM, and 32-cross QAM schemes are derived. For different QAM constellations, a comparative ASER analysis is also illustrated. Furthermore, the impact of TS factor, PS ratio, energy conversion efficiency, NLPA, and threshold data-rates on the considered network is also highlighted. Finally, Monte-Carlo simulations are performed for validation of the derived analytical expressions.