What is the solution to recurrent doubt in prayer, such as forgetting to place the nose on the ground, or the number of prostrations, or the takbir, and what is the legal position regarding this waswas (whispering from Satan)?

The solution is to ignore the whispers and pay no attention to them. Whispers about omitting a pillar of prayer do not necessitate repeating it. Rather, you must not succumb to the whispers and not repeat the prayer, no matter how much you doubt having omitted any of its pillars or obligatory parts, for that is Allah's ruling concerning you.