The Fornax Deep Survey Dwarf galaxy Catalog (FDSDC) includes 564 dwarf galaxies in the Fornax cluster and the in-falling Fornax A subgroup. We use the FDSDC galaxies for statistical analysis of the structural and stellar population differences in the range of galactic environments within the Fornax cluster. We present the standard scaling relations for the dwarfs and analyze trends as a function of cluster-centric radius. We find a different behavior for the bright dwarfs (-18.5 mag < M$_r$ < -16 mag) as compared to the fainter ones (M$_r$ > -16 mag): While considering galaxies in the same magnitude-bins, we find that, while for fainter dwarfs the g-r color is redder for lower surface brightness objects (as expected from fading stellar populations), for brighter dwarfs the color is redder for the higher surface brightness and higher Sersic n objects. The trend of the bright dwarfs might be explained by those galaxies being affected by harassment and by slower quenching of star formation in their inner parts. As the fraction of early-type dwarfs with respect to late-types increases toward the central parts of the cluster, the color-surface brightness trends are also manifested in the cluster-centric trends, confirming that it is indeed the environment that changes the galaxies. We also estimate the strengths of the ram-pressure stripping, tidal disruption, and harassment in the Fornax cluster, and find that our observations are consistent with the theoretically expected ranges of galaxy properties where each of those mechanisms dominate. We furthermore find that the luminosity function, color-magnitude relation, and axis-ratio distribution of the dwarfs in the center of the Fornax cluster are similar to those in the center of the Virgo cluster.