Is Sujud As-Sahw (prostration of forgetfulness) obligatory if the recitation of Al-Fatiha and the final Tashahhud was repeated due to doubt regarding parts of them, and Sujud As-Sahw was performed after the Tasleem (salutation of peace)? And is Sujud As-Sahw valid after the Tasleem in this case?

Whoever doubts having omitted something from the Fatiha, and repeats it before bowing, or doubts having omitted something from the final Tashahhud, and repeats it before saluting, is not required to perform the prostration of forgetfulness (Sujud al-Sahw). The general rule is that if one finishes the Fatiha and then doubts having recited a verse from it, that doubt is to be disregarded. However, if one doubts this before completing the Fatiha, then one should restart the Fatiha. The prostration of forgetfulness is not required for repeating the Fatiha or the Tashahhud, because intentionally repeating them does not invalidate the prayer. The Malikis held that if one repeated an obligatory utterance, such as the Fatiha or the final Tashahhud, one should perform the prostration of forgetfulness. As for someone who, out of forgetfulness, recites something in the Fatiha that alters its meaning, such as pronouncing the letter 'ta' in 'an'amta' with a dammah, the Shafi'is mandate the prostration of forgetfulness, whereas the Hanbalis do not.