Is it permissible to recite the glorifications (Subhanallah, Walhamdulillah, Wala Ilaha Illallah, Wallahu Akbar) in every rak'ah of the prayers after Al-Fatiha and a surah, whether in the first and second rak'ahs, or the third and fourth rak'ahs after reciting Al-Fatiha only, and in Fajr prayers and sunnah prayers, knowing that I glorify in bowing (ruku'), prostration (sujud), and after the first and last tashahhud?

Reciting and glorifying (Allah) while standing before bowing (rukūʿ) does not invalidate the prayer if done intentionally, but performing it is not legislated. However, if done out of forgetfulness, then according to the Hanbalis, prostration of forgetfulness (sujūd al-sahw) is sunnah (definition), because it is a prescribed utterance in prayer in general. But if the worshiper utters a remembrance or supplication for which there is no religious textual evidence, then prostration of forgetfulness is not legislated for him.