Does repeating the first prayer nullify the original prayer, thereby making it obligatory to repeat it even if the new prayer was not completed? And how can one get rid of this doubt in prayer?

This difficulty stems from indulging in whispers (waswas) and not striving against them. You must not indulge in these whispers and turn away from them, for they are from Satan. Approach your prayer with humility, and if Satan whispers to you to interrupt it, or to doubt the takbir, intention, or Al-Fatiha, pay no attention to that and continue your prayer. After finishing the prayer, do not respond to him if he orders you to repeat it; rather, say: "I have prayed my prayer correctly," and seek refuge in Allah from his evil. This decision is correct, but you are making it too late. You are not required to continue with the repeated prayer, for the obligatory prayer has already been performed. Pray the prayer once and do not interrupt it in response to whispers, then do not think about repeating it, and by doing so, you will find peace.