And if there was a difference if the propagational mode of the electric field in the crystal is longitudinal or transverse.
Why does a ionic crystal polarize more at low frequencies rather than at high ones?
Ionic polarization involves displacement of ions, which have some mass and therefore require some time to change their position. So, as the frequency of the applied electric field increases, the response of the ions deceases and, with it, the degree of polarization.
And if there was a difference if the propagation mode of the electric field in the crystal is longitudinal or transverse.
In free space, EM waves are always transverse. When confined, they may acquire a longitudinal component, but it would depend, among other things, on the geometry, so more information (and more expertise in this field) would be required to answer this part of the question.