Not quite. When used with な it's an adjective, but with と it's an adverb. This means that in this sentence, it doesn't modify 世話 but して. (The meaning doesn't change though - in this case)
Yeah, it's like "to provide care for farm products variously (= いろいろと)" vs. "to provide various (= いろいろな) care for farm products" in English. This と is used to express a state when using with adverbs. The meaning is almost the same even if と isn't there.