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1. In general, Status Quo Is God for "This fact cannot change." In Mr. Coyote's case, Failure Is the Only Option.
2. I'm not familiar with this one. It might depend on why it's kept secret and how hard anyone is trying to figure it out. Running Gag comes to mind if it's played for laughs. Running gags, by definition, almost never get "resolved".
If the entire show is based around a mystery and once it's solved, there is no more show, then it's a Driving Question. (A Driving Question may be solved in the series finale though.)
Edited by KD

Rules established by the creator that the work must follow, such as “the coyote must never catch the road runner” or “the krabby patty secret formula must never be revealed.”