1) You suffer effects other than damage regardless if the damage is reduced to zero or not.
2) Resistance doesn't key off the keywords of powers, but off of damage types. Usually they are the same thing, but there are powers that have types that do not completely coincide with the damage. For example, Prismatic Spray has three different Hit components, and only one of them actually deals fire damage despite the power having the Fire keyword.
3) Immunity, however, only concerns power's keywords, so something immune to fire -would- negate ALL the effects of a power with the Fire Keyword, even the parts that are not dealing fire damage.