Is the prayer valid and is one held accountable for saying "Allahu Akbar" before reciting (the Fatiha), or for not saying "Allahu Akbar" when rising from prostration, while being unaware and not intending to do so?

Your prayer is valid and sufficient, and there is no sin upon you. The verbal addition, which is "a takbir before the tasmee‘ (saying 'Sami‘ Allahu liman hamidah')", does not invalidate the prayer, even if there is a difference of opinion regarding the permissibility of performing the prostration of forgetfulness (sujood as-sahw) for it. And performing the prostration of forgetfulness in an incorrect place due to ignorance does not invalidate the prayer. It is obligatory to learn the rulings of individual obligations (furood al-ayn), such as prayer and purification.