Does the prayer or fasting become void by intending to complete it and then inquiring about its validity, and repeating it if it was invalid?

The intention mentioned does not invalidate the prayer, because the questioner did not intend to قطع (terminate) the act of worship or hesitate in it. Rather, he intended to repeat the prayer if its invalidity became apparent, and this does not affect the soundness of the prayer. It is advised to turn away from whisperings (waswas) and ignore them.