Does hesitation in the intention for prayer—due to doubt about wudu—invalidate the prayer and necessitate its repetition, or does it not affect it? And does completing the prayer with the intention of repeating it later fulfill the obligation? If a worshiper repeats Dhuhr prayer due to doubt, is he then required to repeat Asr and Maghrib prayers which he prayed after Dhuhr?

The way to treat whisperings (waswas (definition)) is to ignore them, pay them no mind, and disregard them. No matter how often they occur to you, they have no effect on repeating the prayer, whether before or during it. This is not the kind of hesitation in intention that invalidates the prayer; rather, it is pure whisperings that should not be given any attention. You are not required to repeat any of the prayers you asked about. You must resist these whisperings and not give in to them.