How come catalysts are able to speed up the reaction without themselves getting consumed?

SN2 is a bimolecular reaction. This is because as per the rate law,
Rate = k [substrate] [nucleophile]

Here, the rate determining step is dependent on both substrate and nucleophile, unlike SN1 who only involves substrate. Therefore, SN2 is proved to be bimolecular.

Yes, the phase of the reactant (solid, liquid or gas) actually affects the rate of a reaction. Gases and Liquids tend to move more freely and effectively as compared to solids, which increaes the frequency of particles colliding with each other.