The Nuclotron-based Ion Collider fAcility (NICA) project is under active realization at the Joint Institute for Nuclear Research (JINR, Dubna). The main goal of the project is experimental study of baryon rich QCD matter in heavy ion (up to Au) collisions at centre-of-mass energies up to 11 GeV per nucleon. Two modes of the operation is foreseen, collider mode and extracted beams, with the two detectors, MPD and BM{\at}N. In the collider mode the average luminosity is $L = 10^{27} cm^{-2} s^{-1}$ for Au(79+). Extracted beams of various nuclei species with maximum momenta 13 GeV/c (for protons) will be available. The NICA project also foresees a study of spin physics with the detector SPD with extracted and colliding beams of polarized deuterons and protons at centre-of-mass energies up to 27 GeV (for protons). The NICA experimental program allows to search for possible signs of the phase transitions and critical phenomena as well as to shed light on the problem of nucleon spin structure. Hereafter, feasibility studies of the observables, which are most sensitive to such phenomena, are presented.