What is the correct way of saying the Takbir when rising from prostration to stand for the third Rak'ah, and must the prayer be repeated if the Takbir was said twice in this case?

The standing for the third rak'ah in a four-rak'ah prayer and the Maghrib prayer is from the Tashahhud, and the takbir should be pronounced while standing up for it. The proof for this is the hadith of Abu Hurairah, agreed upon [by Bukhari and Muslim], regarding the description of the Prophet's prayer, peace and blessings be upon him: "And he would say the takbir when he stood up from the second [rak'ah] after sitting." Imam An-Nawawi clarified that this is the view of the majority. Your prayer is valid, and there is no need to repeat it merely for repeating the takbir. The questioner is advised to avoid whisperings [waswasah].