The Spin Physics Detector (SPD) at the Nuclotron-based Ion Collider fAcility (NICA) is designed to study nucleon spin structure in the three dimensions. With capabilities to collide polarized protons (up to √s = 27 GeV) with peak design luminosity 10³² cm^–2 s^–1, the experiment will allow measurements of cross-sections and spin asymmetries that are sensitive to the unpolarized and various polarized gluon distributions inside the nucleons. In the kinematic regime to be probed by the SPD, the leading mechanism of direct photon and charmed D meson production in proton-proton collisions is dominated by interactions involving gluons. This work presents methodology and feasibility of meaningful asymmetry measurements in the two channels at the SPD experiment and their impacts on the current models describing various polarized gluon distributions (i. e. helicity, Sivers).