"He often cooks."
Translation:On często gotuje.
I assume "Często on gotuje" must be wrong because it sounds awkward? Can I generalize this to say that the adverb should immediately precede the verb? Or is it not that simple.
no adverb does not have to "immediately precede the verb", but the sentence you wrote means "it's him who often cooks". splitting adverb and verb happens for two reasons 1) emphasis 2) finding place for words that should not be at the end.