Is it permissible to recite the first verse of Surat Al-Fatihah as "Bismi Allāh al-Raḥmān… al-Raḥīm" by pausing and vocalizing the last letters with a Sukūn, and by pronouncing the hamzat qaṭʿ at the beginning of "al-Raḥmān" and "al-Raḥīm"? And is it permissible in the Tashahhud to recite "wa ‘alā ‘ibādi Allāh al-ṣāliḥīn" by vocalizing the letter Hā’ in the word Allāh with a Sukūn, and by pronouncing the hamzat qaṭʿ at the beginning of "al-ṣāliḥīn"?

You must ignore the obsessive thoughts that afflict you and recite the Qur’an naturally without scrutinizing the articulation points of the letters. This excessive scrutiny is not from the prophetic guidance and will lead you into hardship and difficulty. Furthermore, your described method of recitation does not invalidate the prayer, even though it is not from the guidance of the Prophet (peace be upon him). The Pious Predecessors prohibited extremism and exaggeration in pronouncing letters, because it is blameworthy.