Falls pose a significant risk to the health and wellbeing of older adults, driving the development of various fall detection systems. Existing solutions have explored wearable and vision sensors, while non-invasive RF-based approaches have raised a growing interest due to their convenience and privacy considerations. Despite major advancements in RF-based passive estimation, current approaches still face challenges in handling complex real-world scenarios. They often lack the ability to generalize to new domains (i.e., people, position, environment), and struggle to accurately detect and localize a fallen person in the presence of unknown activities from nearby objects (e.g., pet animal and robot vacuum cleaner) or persons. To address these challenges, we present mm-Fall, a novel mmWave-based non-invasive fall detection system that utilizes Range-Angle (RA) energy maps to separate and localize multiple moving targets, and further accurately estimate their states. Unlike previous approaches, mm-Fall is capable of working with new domains and effectively distinguishing falls from non-fall motions that may appear similar. Additionally, it performs well in challenging conditions, such as poor lighting and occluded scenarios. Our design of mm-Fall is evaluated in 13 environments with over 16 individuals performing 24+ types of motions. The results demonstrate an impressive average recall of 0.969 and precision of 0.996 in detecting falls, whether involving single or multiple moving targets simultaneously. The code and dataset will be made publicly available.