In this paper we study thermodynamic properties of dense cold SU(2) QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to Nf=2 quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region μ∈(0,2000) MeV. It is found that in the region μ∈(0,540) MeV the system is well described by the ChPT predictions. In the region μ>540 MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical potentials μ>900 MeV we observe formation of the Fermi sphere, and the system is similar to the one described by the Bardeen-Cooper-Schrieffer theory where the diquarks play a role of Cooper pairs. In order to study how nonzero baryon density influences the gluon background we calculate chromoelectric and chromomagnetic fields, as well as the topological susceptibility. We find that the chromoelectric field and the topological susceptibility decrease, whereas the chromomagnetic field increases with rising of baryon chemical potential. Finally we study the equation of state of dense two-color quark matter.