We study how a magnetic field induced by colliding nuclei influences both heavy quark (HQ) potential and HQ momentum diffusion coefficients beyond the lowest Landau level approximation. By means of real-time hard thermal loop resummed technique combined with dimension two gluon condensate, the effective gluon propagator describing both perturbative and nonperturbative QCD nature at finite temperature and magnetic field are obtained. We find that HQ momentum diffusion coefficients in magnetized QCD medium become anisotropic, and with increasing temperature, the higher Landau levels become significant, which leads to the reduction of the anisotropic ratio (> 1) and even overturn the behavior (< 1) at high temperature. The nonperturbative (perturbative) contribution of HQ momentum diffusion coefficient in the low (high) temperature is dominant. And the anisotropy feature of the real part of the potential is essentially encoded in angular dependent Coulomb coupling and string tension. Whereas, the imaginary part of the potential from quark-loop in this work displays a significant anisotropy even though using the angular-independent Coulomb coupling and string tension. Furthermore, we study the magnetic response of viscous quark matter, which is manifested in the non-equilibrium distribution function of (anti-)quark by solving Boltzmann equation within the relaxation time approximation. We find the anisotropy ratio is almost insensitive to the magnetized bulk viscosity, although HQ momentum diffusion coefficient and HQ potential itself have visible changes.