They can, but it would be in there best interest to provide more than just the flake you buy at big boxes. A good cichlid flake alternated with a good veggie flake like spirulina would be OK.
If you want SA~ as mentioned before there are rams and apistos. Also, there are many species of Laetacara(curviceps, dorsigera,thayeri) available to the hobby. Rainbow cichlids are another option as are keyholes.
If you are looking for African riverine~ there are many species and variants of Pelvicachromis available with kribs(pulcher) being the most common. Other species of Pelvicachromis available are: taeniatus, humilis, roloffi, rubrolabiatus, sacrimontis, signatus and subocellatus. The african butterfly cichlid (Anomalochromis thomasi) is a beautiful dwarf.
Since this is your first time to keep cichlids, you might want to avoid the rift lake cichlids for the time being as they can be a very aggressive group. A single species of the the shellies would be pretty good though. Just do your research on all of the dwarf cichlids before you decide what species you would like.
As far as tankmates go, there are many options out there from tetras, rasboras, hatchets and cory catfish and plecos. Although I would not put those with rifties except for maybe bristlenose plecos. Some syno. catfish could work with those.