A UV sterilizer kills free floating algae, algae spores, and some parasites such as ich. It has no effect on algae that attach to glass or decor. UV light is very destructive to DNA. However, UV sterilizers are designed so that neither you nor your fish are ever exposed to harmful UV light - just the water that passes through the unit.
I wouldn't consider it an essential piece of equipment for the FW tank.
RO water is commonly used in SW tanks as you probably already know. In FW, it's only needed if your tap water is extremely hard or contains very high nitrates. Some people with well water find it necessary to mix RO with their tap water.