This study presents a comprehensive investigation of the coupled nonlinear dynamic and thermal behavior of composite rotating disc brakes with varying geometric configurations and composite fiber orientations. A hybrid simulation framework combining high-fidelity finite element modeling (FEM), reduced-order modeling (ROM), and physics-informed machine learning (PIML) is developed to efficiently predict the thermo-mechanical response while capturing nonlinear interactions. Parametric analyses are conducted for discs with outer radii R_o=120\mathrm{-}1801mm, thicknesses t_d=8\mathrm{-}16m1, and fiber orientations \theta_f = 0°, 45°, 90°, under rotational speeds of 1000-8000 rpm and contact pressures of 0.5-3.0 MPa. Results demonstrate that vibration amplitudes increase up to 8.9 µm in thin, large discs with \theta_f = 90°, coinciding with thermal hot-spots reaching 430°C. Radial temperature gradients dominate (up to 6.5°C/mm) and correlate with regions of peak vibration, highlighting the critical thermo-mechanical coupling. Nonlinear interactions induce frequency shifts, mode coupling, and localized vibration amplification, emphasizing the necessity of coupled analysis in design optimization. The hybrid framework reduces computational cost by 80-85%, with simulation times of 3.8-4.4 hours compared to 18.8-22.3 hours for full FEM, while maintaining more than 98% prediction accuracy. The study identifies optimal combinations of disc geometry and fiber orientation to mitigate thermal stress and mechanical instability, providing a robust tool for design, optimization, and predictive analysis of high-performance composite disc brakes.