Is the prayer valid if performed with the aforementioned 20 pillars?

The prayer mentioned is generally valid, but important matters must be noted: Uttering the intention verbally is an innovation (bid'ah); the Sunnah is to intend with the heart only. Reciting a surah after Al-Fatiha is a Sunnah, not a pillar. The remembrance for bowing is "Subhana Rabbiyal-Azim (Glory be to my Lord, the Most Great)," and for prostration is "Subhana Rabbiyal-A'la (Glory be to my Lord, the Most High)," both of which are obligatory according to the Hanbalis. The remembrance upon rising from bowing is "Sami'a Allahu liman hamidah (Allah hears the one who praises Him)" for the Imam and the one praying alone, and what is said during standing upright is "Rabbana wa lakal-hamd (Our Lord, and to You be praise)," and what is said between the two prostrations is "Rabbighfir li (My Lord, forgive me)," all of which are obligatory according to the Hanbalis. What is legislated in the Tashahhud is to say: "As-salamu 'alayka ayyuhan-Nabiyyu (Peace be upon you, O Prophet)." The four supplications for seeking refuge (ta'awwudhat) are obligatory in the last Tashahhud, as it is authentically reported from the Prophet (peace be upon him) that the salutation is two salutations.