No, these interactions are not described by molecular mechanics force fields. For that, you should move to quantum mechanical methods, for proteins more likely semi-empirical ones. The impact of such interactions is difficult to extrapolate. In some situations the impact is probably high, but in other situations low. Also, there are some works that suggest that, in some scenarios, the interaction energies calculated by molecular mechanics is well correlated to the quantum mechanics. If you have some indications of this interactions, a combination of molecular mechanics to quantum mechanics would be recommended, by semi-empirical calculation of frames of the entire protein or some QM/MM calculation treating the region of interest in que QM part.
This is a very good suggestion. To some extent, pi-pi interactions are catered for under the general heading of VdW interactions (L-J or similar potential) but these do not capture the directionality inherent in pi-pi interactions, which is certain ways resemble hydrogen bonds (which can be regarded as an example of n-sigma* interactions). So a correction for pi-pi interactions along the lines of hydrogen-bond term in the force-field would be useful. A cation-pi term is tricky unless you know "where" the cation is. Also, there is not really any directionality in that interaction. If we still had Peter Kollman with us, these things would have been done.