Why Christianity?

[orangebox21]

The Islamic god claims to be the final [and corrected] revelation of Yaweh.

The question is why would an omniscient, omnipotent and eternal being not get it's first revelation correct? Why would it need a second, with the christian coming of christ,

The coming of Christ is not a "correction" but a fulfillment of what was promised in the OT. It's a continuation.

and a third, with the revelation on the Arab peninsula?

If it's the same god, then yes that would be a good question.  If not, then the question is nonsensical.