This paper develops a unified framework to maximize the network sum-rate in a multi-user, multi-BS downlink terahertz (THz) network by optimizing user associations, number and bandwidth of sub-bands in a THz transmission window (TW), bandwidth of leading and trailing edge-bands in a TW, sub-band assignment, and power allocations. The proposed framework incorporates multi-connectivity and captures the impact of molecular absorption coefficient variations in a TW, beam-squint, molecular absorption noise, and link blockages. To make the problem tractable, we first propose a convex approximation of the molecular absorption coefficient using curve fitting in a TW, determine the feasible bandwidths of the leading and trailing edge-bands, and then derive closed-form optimal solution for the number of sub-bands considering beam-squint constraints. We then decompose joint user associations, sub-band assignment, and power allocation problem into two sub-problems, i.e., \textbf{(i)} joint user association and sub-band assignment, and \textbf{(ii)} power allocation. To solve the former problem, we analytically prove the unimodularity of the constraint matrix which enables us to relax the integer constraint without loss of optimality. To solve power allocation sub-problem, a fractional programming (FP)-based centralized solution as well as an alternating direction method of multipliers (ADMM)-based light-weight distributed solution is proposed. The overall problem is then solved using alternating optimization until convergence. Complexity analysis of the algorithms and numerical convergence are presented. Numerical findings validate the effectiveness of the proposed algorithms and extract useful insights about the interplay of the density of base stations (BSs), Average order of multi-connectivity (AOM), molecular absorption, {hardware impairment}, {imperfect CSI}, and link blockages.