What is the interpretation of the actions and meaning of salah (prayer), and are the aforementioned hadiths that speak of the interpretation of salah authentic?

The prayer was legislated for the establishment of the remembrance of Allah Almighty, and all its actions embody the meaning of humility and worship of Allah. It is not permissible to lie in its interpretation and to engage in ugly affectation. The mentioned narration attributed to Ali, may Allah be pleased with him, is fabricated and has no basis. The signs of fabrication are evident, such as the statement that whoever does not know the interpretation of prayer, their prayer is deficient. This is a lie against Allah and His Messenger, for the Prophet, may Allah's prayers and peace be upon him, did not mention any of these interpretations to his Companions, and he taught the one who prayed badly the manner of prayer without mentioning interpretations to him.

The two books referred to are circulated on websites belonging to innovators (ahl al-bid'ah), so one must be cautious of them. One should read what is trustworthy in its creed and religion. Ibn al-Qayyim al-Jawziyya's book "Asrar al-Salat" (Secrets of Prayer) suffices in place of them.