Are supplications of obsessive whisperings (waswas) to oneself for harm, especially during times ofanswered prayer, answered?

What you have mentioned are mere whispers (waswas) that have no consequence. Your duty is to disregard them and not pay them any attention, for giving in to these whispers has dire consequences. What helps in this regard is seeking Allah's help, truly resorting to Him, and supplicating frequently.