A method allowing studies the hadronic matter at early stage of the evolution in A+A collisions is developed. It is based on an interferometry analysis of approximately conserved values such as the averaged phase-space density (APSD) and the specific entropy of thermal pions. The plateau founded in the APSD behavior vs collision energy at SPS is associated, apparently, with the deconfinement phase transition at low SPS energies; a saturation of this quantity at the RHIC energies indicates the limiting Hagedorn temperature for hadronic matter. An anomalously high rate of an entropy increase found at the SPS interval of energies can be interpreted as a manifestation of the QCD critical end point, while at the RHIC energies the entropy behavior supports hypothesis of crossover. A detail analysis of a behavior of the interferometry volumes vs energy and the initial system extent in A+A collisions is done. The results shed light on the HBT puzzle.