In this paper, we analyze the performance of an amplify-and-forward (AF) two-way relaying system, where two sources exchange information via the aid of an intermediate relay that is selected among multiple relays according to max-min criterion. We consider a practical scenario, where one source-relay link undergoes Rician fading, and the other source-relay link is subject to Rayleigh fading. To be specific, we derive a tight lower bound for the outage probability. From this lower bound, the asymptotic outage probability and average symbol error rate (SER) expressions are derived to gain insight into the system performance at high signal-to-noise ratio (SNR) region. Furthermore, we investigate the optimal power allocation (PA) with fixed relay location (RL), optimal RL with fixed PA and joint optimization of PA and RL to minimize the outage probability and average SER. The analytical expressions are verified through Monte Carlo simulations, where the positive impact of Rician factor on the system performance is also illustrated. Simulation results also validate the effectiveness of the proposed PA and relay positioning schemes.