Must someone who doubted whether his fingers touched the ground during prostration in prayer, then confirmed a month later that they did not, repeat the prayers he performed, the number of which he does not know?

One must cast off whispers (waswas) and turn away from them. Doubt after completing an act of worship does not affect its validity. If a worshipper prostrates on part of a limb, their prayer is valid. And if they do not prostrate on their hands or feet at all, their prayer is valid according to some scholars.