What is the ruling on the prayer of someone who doubted which rak'ah she was in, then she strongly presumed she was in the third rak'ah and forgot the first tashahhud, so she completed her prayer and performed the prostrations of forgetfulness (sujud al-sahw)?

If doubts become frequent, to the point of being like obsessive whispers (waswas), then they should be ignored, and the prostration of forgetfulness (sujud al-sahw) is not required. Whoever doubts a rak'ah (unit of prayer) and it becomes apparent to him that he is in the third rak'ah, then his prayer is sound, and he is not required to perform sujud al-sahw. Similarly, one does not prostrate for a doubt that has dissipated and it has become clear that he was correct. As for the matter of omitting the first tashahhud, sujud al-sahw is not required with frequent doubts, unless one is certain of its omission, in which case he performs sujud al-sahw. The prayer is valid in all cases.