Joker's wild:
Those are good questions! The checks are for use to assure that systems and items are working properly, and should be used whenever the pilot needs to assess proper operation, but they are not normal procedures. Some of the checks involve disabling or shutting down systems. In such cases, it is not at all a bright idea with passengers aboard, or when the flight situation might deem the action unwise (in the pattern at LHR, or IMC over New York, for example).
I believe that the pilot should refrain from Non-Normal procedures with passengers, especially if on a Pt 135 ticket, unless unusual circumstances dictate.
As is typical nobody would say a thing except if something bad occurs, then there will be 1,000 judges to asssess how good a decision it was.