Is it permissible to ignore and forgo repeating the takbirat, reciting the Fatiha, and performing prostration when in doubt and experiencing waswas during prayer?

You must ignore these whisperings and completely turn away from them. When you pray, say the opening takbir once, loud enough for you to hear yourself. Recite the opening supplication (dua al-istiftah) and Surat al-Fatiha in the same manner, without repeating verses or words. If you doubt the number of prostrations, make them two and do not perform the prostration of forgetfulness (sujud al-sahw). Ignoring these whisperings is the best cure for them.