Using the strong dispersive coupling to a high-cooperativity cavity, we demonstrate fast and nondestructive number-resolved detection of atoms in optical tweezers. We observe individual atom-atom collisions, quantum state jumps, and atom loss events with a time resolution of 100 μs through continuous measurement of cavity transmission. Using adaptive feedback control in combination with the nondestructive measurements, we further prepare a single atom with 92(2)% probability.