In this work we developed a mathematical model and a simulation platform for a fish-inspired robotic template, namely Magnetic, Modular, Undulatory Robotics ($μ$Bots). Through this platform, we systematically explored the effects of design and fluid parameters on the swimming performance via reinforcement learning. The mathematical model was composed of two interacting subsystems, the robot dynamics and the hydrodynamics, and the hydrodynamic model consisted of reactive components (added-mass and pressure forces) and resistive components (drag and friction forces), which were then nondimensionalized for deriving key "control parameters" of robot-fluid interaction. The $μ$Bot was actuated via magnetic actuators controlled with harmonic voltage signals, which were optimized via EM-based Policy Hyper Parameter Exploration (EPHE) to maximize swimming speed. By varying the control parameters, total 36 cases with different robot template variations (Number of Actuation (NoA) and stiffness) and hydrodynamic parameters were simulated and optimized via EPHE. Results showed that wavelength of optimized gaits (i.e., traveling wave along body) was independent of template variations and hydrodynamic parameters. Higher NoA yielded higher speed but lower speed per body length however with diminishing gain and lower speed per body length. Body and caudal-fin gait dynamics were dominated by the interaction among fluid added-mass, spring, and actuation torque, with negligible contribution from fluid resistive drag. In contrast, thrust generation was dominated by pressure force acting on caudal fin, as steady swimming resulted from a balance between resistive force and pressure force, with minor contributions from added-mass and body drag forces. Therefore, added-mass force only indirectly affected the thrust generation and swimming speed via the caudal fin dynamics.