Supersymmetry being a symmetry just imposes additional restrictions on the "space of viable QFTs", which means that the number of supersymmetric Lagrangians is reduced compared to the number of "conventional" Lagrangians. Supersymmetry should therefore not change the basic (Feynman) rules that give for example a recipe for calculating scattering amplitudes from the terms present in the Lagrangian of the theory. In the same way, R-symmetry disallows certain interaction terms in the Superlagrangian, that would violate lepton and baryon number conservation.
In the MSSM, the number of particles is doupled compared to the content of the SM and it has 5 potentially observable higgs scalars. Since the superpartners differ from the SM particles just by their spin and their mass (but the charge is the same), they interact via the same coupling constants which are present in the SM too. So the basic Feynman rules to calculate things in the MSSM are not changed, but there are additional sparticles to play with. At the level of Feynman diagrams, R-symmetry has the effect that there are no interactions coupling a single superpartner to two SM particles.
However, in the context of the superspace formalism, which is very useful and efficient to derive supersymmetric "ordinary Lagrangians" from Superlagrangians, there exists a generalization of the well known Feynman diagrams called Supergraphs. These are diagrams similar to the Feynman diagrams, wherein the ordinary quantum fields are replaced by superfields (that depend in addition to the conventional spacetime coordinates on Grassmanian coordinates), to calculate things from the allowed interactions between the superfields described in the Superlagrangian.