The first polyoxorhenate(VII) compound, pyrazolium polyoxorhenate ((C4N2H5)2Re4O15), and two new rhenium(VII) and technetium(VII) salts have been synthesized and studied. The structure of Tc2O7 has been reinvestigated. The [Re4O15]2- polyoxoanion contains four Re(VII) atoms: one with an octahedral environment and three with a tetrahedral environment. Polyoxorhenate is formed in the presence of a buffering agent, pyrazole, the latter maintaining pH = 2.5 during the formation of crystals. The [Re4O15]2- polyoxoanion has novel stoichiometry and the cis-conformation, likely due to the stabilizing intramolecular nonvalence interactions. For the first time, intramolecular interactions of the Re···O, Re···μ-O, and O···O are described (previously known were only intermolecular ones). In all of the compounds, intermolecular Re···O interactions are observed, which, however, in other compounds, do not lead to the formation of polyoxometalates. The Hirshfeld surface analysis showed that the main contribution to intermolecular interactions is made by the O···H/H···O contacts, van der Waals interactions of the H···H for cations, and the O···O for anions. DFT calculations of the [Re4O15]2- geometry, compared with the crystallographic data, revealed a deviation in the angles. Mass spectroscopy of the red polyoxometalate [Tc20O68]4- was carried out for the first time. Comparison of the results of MALDI and LI for the first known polyoxometalates of the manganese subgroup made it possible to find general patterns of oligomerization for rhenium and technetium compounds. The ESI-MS and LI-MS methods applied to solution and crystals Re compounds made it possible to prove rhenium being able to form not only [Re4O15]2- but also heavier polyoxoanions.