The fact that the tamper material was uranium enriched in U was deduced based on the final fission reaction fragments detected in the radiochemical analysis, conclusively shown by the U found by the Japanese in the shot debris.
2.
Nuclear tests, including underground tests that vent into the atmosphere, produce fallout that not only indicates that a nuclear event has taken place, but, through radiochemical analysis of radionuclides in the fallout, characterize the technology and source of the device.