After having published the first thunderstorm ground enhancements (TGEs) catalog to explain long-lasting TGEs, we address here problems pertaining to TGE evolution (shape) and atmospheric conditions supporting the origination of the relativistic runaway electron avalanches. We also address the question of radon progeny gamma radiation and its contribution to overall TGE flux. We demonstrate that by using detectors with different energy thresholds we can identify and reliably separate both mechanisms of TGE origination. An analysis of measured energy spectra of TGEs reveals contributions of both processes to the TGE temporal evolution and shape. We also confirm the model of radon progeny radiation during a thunderstorm.