Is the aforementioned wording of the Tashahhud correct and does it affect the validity of the prayer?

The wording mentioned in the Tashahhud is not sufficient to fulfill the testimony that Muhammad is the Messenger of Allah. The minimum wording of the Tashahhud that is sufficient—by scholarly consensus—must include: "All greetings and acts of worship are for Allah. Peace be upon you, O Prophet, and Allah's mercy and blessings. Peace be upon us and upon the righteous servants of Allah. I bear witness that there is no god but Allah, and I bear witness that Muhammad is the Messenger of Allah." As for the Ibrahimiyyah prayer, the wording mentioned therein is sufficient. The final Tashahhud is a pillar of prayer, and if the worshiper does not recite it with the sufficient wording, their prayer is invalid.