In-band full-duplex (FD) communication has emerged as one of the promising techniques to improve data rates in next generation wireless systems. Typical FD scenarios considered in the literature assume FD base stations (BSs) and half-duplex (HD) users activated either in uplink (UL) or downlink (DL), where inter-user interference (IUI) is treated as noise at the DL user. This paper considers more general FD scenarios where an arbitrary fraction of the users are capable of FD and/or they can perform successive interference cancellation (SIC) to mitigate IUI. Consequently, one user can be activated in either UL or DL (HD-UL and HD-DL modes), or simultaneously in both directions requiring self-interference mitigation (SIM) at that user (FD-SIM mode). Furthermore, two users can be scheduled, one in UL and the other in DL (both operating in HD), where the DL user can treat IUI as noise (FD-IN mode) or perform SIC to mitigate IUI (FD-SIC mode). This paper studies opportunistic mode selection and user scheduling under long-term and short-term temporal fairness in single-carrier and multi-carrier (OFDM) FD systems, with the goal of maximizing system utility (e.g. sum-rate). First, the feasible region of temporal demands is characterized for both long-term and short-term fairness. Subsequently, optimal temporal fair schedulers as well as practical low-complexity online algorithms are devised. Simulation results demonstrate that using SIC to mitigate IUI as well as having FD capability at users can improve FD throughput gains significantly especially, when user distribution is concentrated around a few hotspots.