Efficient path planning and trajectory tracking are central to the safe and autonomous navigation of autonomous underwater vehicles (AUVs) in complex and unknown environments. To address the inherent challenges of safety, smoothness, and exploration efficiency in such settings, this paper presents an integrated framework that synergistically couples three enhanced core modules with complementary innovations. First, improved I-LazyTheta* and A-IRRT* algorithms are developed to incorporate safety margin collision detection and dynamic obstacle avoidance weight regulation, which enable efficient generation of collision-free paths that proactively maintain safe clearance in cluttered 3D spaces. Second, a trajectory tracking module based on a finite-state machine is designed, integrating B-spline optimization and a curvature-adaptive speed control mechanism to ensure high-precision following with guaranteed path smoothness and trackability. Third, a novel 3D autonomous exploration strategy tailored to underwater sonar constraints is constructed, combining frontier point clustering, multi-dimensional information gain evaluation, and traveling salesman problem (TSP) path optimization to achieve efficient unknown environment traversal while significantly reducing redundant detection and energy consumption. The proposed framework supports modular decoupling for independent reuse as well as integrated collaborative operation, offering flexible adaptability to diverse underwater robotic platforms. Simulations demonstrate that the integrated approach achieves superior performance in path safety and tracking accuracy, along with an exploration coverage of 79.08%, validating its effectiveness for robust AUV autonomy in complex underwater scenarios.