The answer to all your questions is, of course, It Depends. You are right that a scale would hardly be useful if the notes could only be played in order. Similarly it would be very limiting if no notes other than those of the scale were permitted. But if the Db in your imaginary scale were repeated over and over, melodically and harmonically, at some point we would have to conclude that this is a (not really) new scale. To conclude whether the music is composed in the A minor pentatonic or C major pentatonic would again depend upon the frequency with which the note A or the note C was heard at important junctures. There could be a music in which it would be impossible to conclude which scale was the predominant one.
Consider how Bach will begin a piece in, say, C minor, and somehow by the end of the first half of the piece we are clearly hearing Eb Major. So the prevailing scale has changed --- although C minor and Eb Major have the same key signature.
