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This letter investigates the effects of imperfect channel state information (CSI) for incident channels and discrete phase-shift design on the performance of full-duplex two-way communication-based reconfigurable intelligent surface (RIS) systems. In order to characterize the system performance, the approximate and asymptotic expressions for the outage probability (OP) and ergodic capacity (EC) are derived. Relying on these analyses, the diversity order, the ergodic slope, and some valuable technical insights regarding performance trends are also deduced. Extensive simulations are provided to corroborate the theoretical analysis. Numerical results show that: 1) the derived analysis can approach well with the simulation results; 2) imperfect CSI leads to the performance floor at high transmit power regimes; 3) better CSI estimation provides significant system performance improvement; and 4) by using 3-bits for …