This work conceives a unified channel estimation and beamforming framework, formulated within the principles of variational Bayesian inference. Recognizing the limitations imposed by hardware constraints, frequency-dependent propagation effects, and the structural restrictions of partially connected architectures in the Terahertz (THz) band, we formulate a dual-wideband channel model incorporating root raised cosine (RRC) pulse shape to account its band-limited nature. To further address the nonlinear distortions introduced by low-resolution ADCs, Bussgang decomposition is employed, enabling a tractable linearized inference process. Unlike conventional techniques, the proposed method accommodates both on-grid and off-grid angular domains, capturing spatial sparsity with improved resolution and robustness. The multi-user (MU) Bayesian Cramér-Rao lower bound is also derived to benchmark the performance of the proposed estimator. Moreover, the framework incorporates a true time delay (TTD)-based hybrid transceiver design that inherently compensates for the beam-squint effect; a frequency-dependent angular deviation that arises due to the fixedphase nature of the conventional beamformer in wideband systems, thereby ensuring accurate directional alignment across all subcarriers. Extensive simulation results validate the effectiveness of the proposed variational Bayesian inference-based estimator and the TTD-enabled beamforming architecture, highlighting their robustness and performance gains under practical wideband THz system.