Planning safe and efficient trajectories through signal-free intersections presents significant challenges for autonomous vehicles (AVs), particularly in dynamic, multi-task environments with unpredictable interactions and an increased possibility of conflicts. This study aims to address these challenges by developing a unified, robust, adaptive framework to ensure safety and efficiency across three distinct intersection movements: left-turn, right-turn, and straight-ahead. Existing methods often struggle to reliably ensure safety and effectively learn multi-task behaviors from demonstrations in such environments. This study proposes a safety-critical planning method that integrates Dynamic High-Order Control Barrier Functions (DHOCBF) with a diffusion-based model, called Dynamic Safety-Critical Diffuser (DSC-Diffuser). The DSC-Diffuser leverages task-guided planning to enhance efficiency, allowing the simultaneous learning of multiple driving tasks from real-world expert demonstrations. Moreover, the incorporation of goal-oriented constraints significantly reduces displacement errors, ensuring precise trajectory execution. To further ensure driving safety in dynamic environments, the proposed DHOCBF framework dynamically adjusts to account for the movements of surrounding vehicles, offering enhanced adaptability and reduce the conservatism compared to traditional control barrier functions. Validity evaluations of DHOCBF, conducted through numerical simulations, demonstrate its robustness in adapting to variations in obstacle velocities, sizes, uncertainties, and locations, effectively maintaining driving safety across a wide range of complex and uncertain scenarios. Comprehensive performance evaluations demonstrate that DSC-Diffuser generates realistic, stable, and generalizable policies, providing flexibility and reliable safety assurance in complex multi-task driving scenarios.