Why is Quran the final word of God?

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Even in the Quran, in some verses Muhammad confesses His sins, and asks God to forgive Him. These verses, although it appears Muhammad has sinned, in reality He did not, but since He represents His people, just as a King who represents His people, He is asking forgiveness for His community, using an indirect mode. It has a wisdom. It is meant to teach His community to ask forgiveness from God, and be humble towards God. Due to God's mercy, He does not wish to directly rebuke the community of believers, so, instead Muhammad is addressed as one who sinned. Bible, likewise, follows same logic in the cases you have referred.

The verses about Mohammad's "sin" according to some hadiths are in context of his Crime as claiming Tawheed and to be a Prophet. He seeks "protection" from God regarding that for himself and believers.

But you are right in another sense our Imams prayed for sinners as if they were themselves the sinners. This is true, and it also has a theme that everyone is everyone, and that we are one soul, for love is not selfish and reason dictates to see value in all humans and not just value yourself above others as this is mathematically wrong.

But I would read the verses of Saul again, it's obvious in the Torah, he becomes envious and evil, and even it says God regrets appointing him in the first place.