With multi-GHz bandwidth, Terahertz (THz) beamforming has drawn increasing attention in the sixth generation (6G) and beyond communications. Existing beamforming designs mainly focus on a compact antenna array where typical communication occurs in the far-field. However, in dense multi-user scenarios, only relying on far-field angle domain fails to distinguish users at similar angles. Therefore, a multi-user widely-spaced array (MU-WSA) is exploited in this paper, which enlarges the near-field region to introduce the additional distance domain, leading to a new paradigm of cross-near-and-far-field (CNFF) communication. Under this paradigm, the CNFF channel model is investigated, based on which the subarray spacing $d_s$ and the number of subarrays $K$ in MU-WSA are optimized to maximize the channel capacity. Then, in sub-connected systems, an alternating optimization (AO) beamforming algorithm is proposed to deal with the special block-diagonal format of the analog precoder. For fully-connected systems, a low-complexity steering-vector reconstruction (SVR)-based algorithm is proposed by constructing specialized steering vectors of MU-WSA. Numerical evaluations show that due to distance domain resolutions, the MU-WSA can improve the SE by over $60$% at a power of $20$dBm compared to the compact array. Additionally, the proposed AO algorithm in the SC system can achieve over 80% of the sum (SE) of the FC system while reducing the number of phase shifters by $K^2$, thereby lowering power consumption. The SVR algorithm in the FC system can achieve over 95% of the upper bound of SE but takes only 10% of the running time of the singular vector decomposition (SVD)-based algorithms.