The structure and dynamics of polymers in confinements (such as porous media, channels and slits) depend not only on the characteristic length scales of the confinements but also on solvent types and interactions between polymers and confinement constituents. In this study, we show by performing both molecular dynamics (MD) and Langevin dynamics (LD) simulations that the lateral diffusion of a single flexible polymer in good solvent in a slit should be determined by a complicated interplay among the slit height (H), solvent types and slit wall roughness. The slit wall roughness is tuned by employing either corrugated walls or smooth walls. We find from simulations that only when solvent molecules are implemented explicitly in MD simulations, the wall roughness makes a qualitative difference in the lateral diffusion coefficient (D||) of the polymer: as H is decreased, D|| increases for smooth walls while D|| decreases for corrugated walls. Such a qualitative difference in D|| should be a solvent-mediated effect, which is not observed for implicit solvent models in LD simulations. The single polymer in the slit with the explicit solvent model follows Zimm dynamics while the polymer follows Rouse dynamics with the implicit solvent models. In the meantime, the wall roughness hardly affects the structure of the polymer in the slit. The density distribution functions of monomers (ρm(z)) and solvent molecules (ρs(z)) do not depend on whether the walls are corrugated or smooth. The radius of gyration (Rg) is also insensitive to the wall roughness. On the other hand, the solvent model give rise to a qualitative difference in ρm(z) and Rg, especially when the height (H) of the slit is small. For sufficiently small values of H, ρm(z) depends on the size of solvent molecules used in the explicit solvent model. However, regardless of the solvent model and wall roughness, the scaling exponent (n) of Rg and the degree of polymerization (N) (i.e., Rg~Nν) changes gradually from 0.6 to 0.75 as H decreases. We also investigate solvent quality effects on static and dynamic properties of a single polymer with explicit solvent in a slit using MD simulations. We show that the density distribution functions of monomers and solvents in a poor solvent are similar to those in a good solvent. We find that wall roughness also affects the lateral diffusion, D|| of the confined polymer in a poor solvent qualitatively. D|| of the confined polymer decreases for corrugated walls and increases for smooth walls as H decreases.