Is the worshiper's raising of his hands after bowing, with their palms facing his face, in accordance with the Sunnah, and if not, what is the correct posture for raising the hands?

It is Sunnah for the worshipper to raise his hands parallel to his shoulders or ears when saying the opening Takbir (Takbirat al-Ihram), when bowing and rising from bowing, and when standing up from the first Tashahhud. The palms should be facing the Qiblah. This is what is authentically reported from the Prophet (peace be upon him).