A fool's errand is a useless piece of work.
A fool's paradise a happy state for which there is no good reason.
The wise fool is a common literary character, a person who appears at first to be unintelligent but then reveals him or herself to possess a grest deal of wisdom. An example of this is Sancho Panza in Cervantes' Don Quixote. Sancho is an uneducated peasant who at first seems to have little sense or experience. However, as the tale unfolds, he reveals himself to possess a wealth of common sense, first expressed through endless proverbs, but then through his own skill. In this sense he provides a comic juxtaposition to Quixote himself, who is highly educated but insane; both of them supply what the other lacks.