Contemporary Internet-of-Things (IoT) devices in general and Internet-of-Vehicles (IoV) networks in specific are taking the benefits from using full-duplex (FD) communication with the help of relay nodes to facilitate data transmission. However, self-interference between transmit and receive antennas at the relay node may cause big trouble if self-interference cancellation (SIC) is not applied. In this paper, a rigorous analysis on the performance of FD two-way relay networks (FDTWRNs) for IoV applications under imperfect conditions is provided. Different from earlier studies on the performance of FDTWRNs where one or two imperfect factors were considered, this work simultaneously takes into account many practical issues in the implementation of the IoV networks at the physical layer, including errors in channel state information at all channel links, imperfect SIC and transceiver hardware impairment at all nodes. For relaying protocol, we consider amplify-and-forward with both fixed-gain (FG) and variable-gain (VG) protocols. The exact closed-form expressions (in terms of the system parameters) of key performance factors such as signal-to-interference-plus-noise-distortion-and-error ratio (SINER), outage probability (OP), achievable data rate (ADR), and average symbol error probabilities (ASEP) of the considered system over Rayleigh fading channels and under the combined effect of imperfect CSI, SIC, and transceiver hardware are derived mathematically using probabilistic model analysis. The correctness of the analysis is then verified by Monte Carlo simulations. Drawing upon both analytical and numerical findings, the efficacy of the FDTWRNs under consideration is meticulously and comprehensively assessed in comparison to its performance in ideal conditions characterized by one or multiple critical factors. The disparity between perfect and imperfect scenarios serves as a valuable metric for appraising the practical viability of the considered FDTWRNs when deployed in practical IoV networks.