Is saying, "I bear witness that there is no god but Allah, and I bear witness that Muhammad is the Messenger of Allah" in the Tashahhud correct, and does omitting the letter waw after "Al-Tahiyyat Lillahi" invalidate the prayer and affect past prayers?

The mentioned Tashahhud is correct, and the prayer is valid, as there are several authentic versions of the Tashahhud narrated from the Prophet, peace be upon him. Among them is what Muslim narrated from Ibn Abbas with the wording: "I bear witness that Muhammad is the Messenger of Allah." It is also permissible to omit "al-salawat al-tayyibat" (the good prayers), as jurists have specified the obligatory minimum amount of Tashahhud, such as Ibn Muflih al-Hanbali and al-Nawawi, stating that the minimum obligatory Tashahhud is: "All greetings 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."