High-quality, large-scale synthetic data from simulations is becoming a cornerstone for pushing the capabilities of robot algorithms. While aerial robotics simulators have evolved to support specialized needs such as fidelity, differentiability, and swarms independently, a unified platform that can synthesize data across all these domains is missing. In this work, we propose Crazyflow, a simulator designed to push the limits of aerial-robotics algorithm development, from model-based to data-driven methods, gradient-based to sampling-based approaches, and single-agent to multi-agent systems. Compared to existing state-of-the-art drone simulators, it achieves speeds more than an order of magnitude faster for a single drone and can simulate thousands of swarms of 4000 drones each. Real-world experiments show Crazyflow supports both analytical-gradient-based policy learning, achieving sub-centimeter trajectory tracking accuracy without domain randomization, and sampling-based obstacle avoidance at speeds exceeding half a billion steps per second. Breaking the traditional train-then-deploy paradigm, we show that its unprecedented speed even enables in-flight reinforcement learning; we demonstrate this by throwing a physical drone into the air and training a recovery policy from scratch in 0.38 seconds, successfully stabilizing the drone. Crazyflow supports multiple levels of simulation abstraction, is directly compatible with all open-source Crazyflie models, and enables rapid reconfiguration across custom drone platforms and applications by providing a light-weight system identification pipeline. By pushing accuracy, speed, and differentiability simultaneously, Crazyflow serves as an open-source resource for synthetic data generation, with emerging capabilities for large-scale parallelization for online, in-execution learning and optimization, opening the door to novel algorithm development.