Usage of low-cost hardware in large antenna arrays and low-power wireless devices in Internet-of-Things (IoT) has led to the degradation of practical beamforming gains due to the underlying hardware impairments like in-phase-and-quadrature-phase imbalance (IQI). To address this timely concern, we present a new nontrivial closed-form expression for the globally-optimal least-squares estimator (LSE) for the IQI-influenced channel between a multiantenna transmitter and single-antenna IoT device. Thereafter, to maximize the realistic transmit beamforming gains, a novel precoder design is derived that accounts for the underlying IQI for maximizing received power in both single and multiuser settings. Lastly, the simulation results, demonstrating a significant -8dB improvement in the mean-squared error of the proposed LSE over existing benchmarks, show that the optimal precoder designing is more critical than accurately estimating IQI-impaired channels. Also, the proposed jointly-optimal LSE and beamformer outperforms the existing designs by providing 24% enhancement in the mean signal power received under IQI.