n this paper, the impact of HWI on channel estimation error (CEE) and their combined impact on the performance of amplify-and-forward variable-gain (AF-VG) two-way relay network (TWRN) has been investigated. The expression for equivalent signal-to-noise plus distortion- anderror ratio (SNDER) at user terminals is derived. This is used to deduce closed-form expressions for the exact analysis of outage probabilities (OP) and tractable formulations for average symbol error rate (SER) taking a Rayleigh block fading channel. For further insights, we perform asymptotic analysis of OP and observe irreducible outage floors which act as fundamental performance limits. This SNDER ceiling acts as an upper limit for practical transmission rates. These derived results are validated using Monte Carlo simulations. Finally, we provide insights into the trade-off between the training length and pilot transmission power to obtain better performance by analyzing the symbol error rate (SER) curves under different training conditions.