1) Yes, almost any type of geometry can be modeled with OptiFDTD. You can use the PBG crystal editor to help you create hexagonal, square or arbitrary lattices. For more information on this tool, have a look at the following webpage: https://optiwave.com/optifdtd-manuals/fdtd-photonic-crystal-and-photonic-band-gap-introduction/
2) The effective refractive index can be calculated using the mode solver included with OptiFDTD: OptiMode. It can be used directly from OptiFDTD’s interface or as a standalone product.