In this paper, the problem of uplink (UL) and downlink (DL) resource optimization, mode selection and power allocation is studied for wireless cellular networks under the assumption of in-band full duplex (IBFD) base stations, non-orthogonal multiple access (NOMA) operation, and queue stability constraints. The problem is formulated as a network utility maximization problem for which a Lyapunov framework is used to decompose it into two disjoint subproblems of auxiliary variable selection and rate maximization. The latter is further decoupled into a user association and mode selection (UAMS) problem and a UL/DL power optimization (UDPO) problem that are solved concurrently. The UAMS problem is modeled as a many-to-one matching problem to associate users to small cell base stations (SBSs) and select transmission mode (half/full-duplex and orthogonal/non-orthogonal multiple access), and an algorithm is proposed to solve the problem converging to a pairwise stable matching. Subsequently, the UDPO problem is formulated as a sequence of convex problems and is solved using the concave-convex procedure. Simulation results demonstrate the effectiveness of the proposed scheme to allocate UL and DL power levels after dynamically selecting the operating mode and the served users, under different traffic intensity conditions, network density, and self-interference cancellation capability. The proposed scheme is shown to achieve up to 63% and 73% of gains in UL and DL packet throughput, and 21% and 17% in UL and DL cell edge throughput, respectively, compared to existing baseline schemes.