This research work addresses the inadequacy of isothermal wall conditions in predicting accurate flow features and thermal effects for multi-component systems. A finite-difference characteristic-based off-lattice Boltzmann method (OLBM) with a source-term-based conjugate heat transfer (CHT) model is used to analyze buoyancy-driven flows in two and three-dimensional cavities. The developed CHT-OLBM solver is verified using analytical solutions and reference data from the literature. The effects of wall conduction on conjugate natural convection (CNC) problems in square and horizontal annular cavities are systematically examined with a solid wall of a non-dimensional thickness of 0.2. The effects of thermal conductivity ratio, ranging from 1 to 100, is studied for the square and horizontal annular cavity problems. Qualitative analysis of the simulation results using isotherms and streaml ines and quantitative analysis of the local fluid-solid interface temperature, solid wall temperature distribution, Nusselt number profiles, overall Nusselt number, and effective Grashof/Rayleigh number are performed. The overall heat transfer reduction inside the cavities due to a solid wall is quantified, and correlations are obtained to represent the overall heat transfer inside both enclosures. The findings demonstrate the significance of CHT analysis, and the CHT-OLBM solver developed in this study can successfully investigate steady/unsteady, and chaotic CNC flows. After studying two-dimensional cavities, three different eddy-viscosity based sub-grid scale (SGS) models and implicit large-eddy simulation (ILES) are assessed for turbulent natural convection in a 3D tall cavity. The SGS models evaluated are the constant coefficient Smagorinsky model (with and without van Driest damping function), the wall-adapting local eddy-viscosity (WALE) model, and the Vreman model. The performance of various SGS models and ILES is evaluated by comparing mean profiles, second-order statistical quantities, SGS activity parameter and local heat transfer statistics with reference direct numerical simulation (DNS) data. Of the tested models, the constant coefficient Smagorinsky model with the van Driest damping function demonstrates superior performance. Upon verifying the turbulence model, the influence of solid wall conduction on turbulent natural convection flow within a 3D tall cavity is investigated. The solid wall has a dimensionless thickness of 0.2 and a solid-to-fluid thermal conductivity ratio of 10. The study evaluates the effects of wall conduction on various turbulent quantities, including mean and second-order statistics, heat transfer rates at the fluid-solid interface, and turbulent kinetic energy budgets. The results indicate a reduction of approximately 6.86 % in overall heat transfer within the cavity attributed to the solid wall's presence.