Is the prayer acceptable if the Basmalah is recited before the Fatiha in the first rak'ah but not in the second, and is the Basmalah considered obligatory before the Fatiha in every rak'ah according to the Hanafis?

Reciting the isti'adha (seeking refuge with Allah) before recitation and the basmala (In the name of Allah) before Al-Fatiha are sunnah (definition). Forgetting them, whether intentionally or unintentionally, does not invalidate the prayer, nor does it necessitate the prostration of forgetfulness (sujood as-sahw). However, it is recommended to perform sujood as-sahw for one who forgets them if it was their habit to recite them. As for the Hanafis, the basmala is a sunnah to be recited silently at the beginning of Al-Fatiha in every rak'ah, but it is not sunnah to recite it between Al-Fatiha and the following surah (definition).