We consider J/Psi meson production in $ep$ deep inelastic scattering in the colour singlet model using the k_T-factorization QCD approach. We investigate the z-, Q^2-, p_T^2-, y^*- and W-dependences of inelastic J/Psi production on different forms of the unintegrated gluon distribution. The p_T^2- and Q^2-dependences of the J/Psi spin aligment parameter alpha are presented also. We compare the theoretical results with recent experimental data taken by the H1 and ZEUS collaborations at HERA. It is shown that experimental study of the polarization J/Psi mesons at Q^2 < 1 {GeV}^2 is an additional test of BFKL gluon dynamics.

14 pages, 8 figures, Talk at International School "Heavy Quark Physics", May 27 - June 5, JINR, Dubna, Russia