Drones have recently emerged as a faster, safer, and cost-efficient way for last-mile deliveries of parcels, particularly for urgent medical deliveries highlighted during the pandemic. This paper addresses a new challenge of multi-parcel delivery with a swarm of energy-aware drones, accounting for time-sensitive customer requirements. Each drone plans an optimal multi-parcel route within its battery-restricted flight range to minimize delivery delays and reduce energy consumption. The problem is tackled by decomposing it into three sub-problems: (1) optimizing depot locations and service areas using K-means clustering; (2) determining the optimal flight range for drones through reinforcement learning; and (3) planning and selecting multi-parcel delivery routes via a new optimized plan selection approach. To integrate these solutions and enhance long-term efficiency, we propose a novel algorithm leveraging actor-critic-based multi-agent deep reinforcement learning. Extensive experimentation using realistic delivery datasets demonstrate an exceptional performance of the proposed algorithm. We provide new insights into economic efficiency (minimize energy consumption), rapid operations (reduce delivery delays and overall execution time), and strategic guidance on depot deployment for practical logistics applications.