In this work, we study the interactions of fast ions with graphene describing the excitations of the electron gas in graphene by a two-dimensional (2D) hydrodynamic model (one-fluid and two-fluid model). The two-fluid model reproduces qualitatively the split of plasmon dispersions into the low-frequency p-electron branch and the high-frequency s+p-electron branch. We calculate the stopping force and the image force on an ion moving parallel to a single sheet of graphene. Numerical results show that the presence of the low-energy, quasiacoustic plasmon in the two-fluid model gives rise to resonant features at low velocities around its 'acoustic' speed, which are not seen in the one-fluid model. The two models give virtually indistinguishable results for both forces at high speeds. Marked differences between the two models in the values of image forces at low speeds can be seen. Numerical results show that the magnitudes of both the stopping and image forces exhibit typical resonance-shaped velocity dependencies, with the peak positions moving to higher velocities for higher distances and with the overall magnitudes decreasing sharply with increasing distances. The second order corrections are found to be small, as expected for fast ions outside the electron gas, but their relative magnitudes should be easily discernible in experiments on ion grazing scattering from graphene. One notices effects which are similar to those obtained earlier for proton channeling in carbon nanotubes.