Is the prayer valid if the worshipper recites silently without hearing themselves, and is it permissible to recite silently by moving the lips without sound, and is the opening "Allahu Akbar" (Takbirat al-Ihram) valid without sound?

Scholars have differed concerning the minimum for audible recitation (sirr) in prayer. Some are of the view that the worshipper must make himself hear, while others hold that it is sufficient to move the tongue while articulating the letters. Based on the second opinion, your prayer is valid and there is no sin upon you if you recite Al-Fatihah, the opening Takbir, or the Taslim by moving your tongue without making a sound.