This paper investigates beamforming techniques for in-band full-duplex multi-cell multi-user (IBFD-MCMU) wireless networks considering hardware impairments (HWIs), channel uncertainty, and limited channel state information (CSI). For the global CSI scenario, we first enhance zero-forcing (ZF), maximum ratio transmission and combining (MRTC), and minimum mean-squared error (MMSE) beamforming to be compatible with multi-antenna users and IBFD base stations. Then, we investigate beamforming schemes for the local CSI assumption where only intra-cell channel knowledge is fully available at the base stations, and inter-cell channels are known statistically due to the limited training resources. With these limitations, two MMSE-based methods are proposed, which regard unknown CSI as random instances (i.e., eMMSE-RI) and noise (i.e., eMMSE-N). We explore the self-interference cancellation (SIC) capability of beamformers and evaluate the performance of these methods in 3GPP scenarios. Numerical results reveal that the enhanced MMSE beamforming can achieve the desired IBFD with low analog SIC depth, inspiring a low-cost IBFD transceiver design. The practical imperfections (e.g., transceiver HWIs, channel uncertainty, limited CSI) decrease the achievable sum rate but do not reduce the IBFD gain. With CSI limitations, eMMSE-RI outperforms eMMSE-N for microcells, where the probability of the presence of LOS is high, whereas eMMSE-N performs better when cell size is enlarged.