Would creating a complete computer simulation of the human brain prove the Church-Turing thesis?
How would you prove that the machine is faithfully simulating a brain? How would you prove that it doesn't matter if you simulate my brain or your brain or somebody else's brain?

Church&ndash;Turing isn't something that can be proven. It's essentially just the statement that Turing machines correspond to the intuitive notion of algorithm and that just isn't a statement of mathematics. The Turing machine is the definition of computability; Church&ndash;Turing is essentially the claim that we picked the right definition, in the sense that choosing any of the reasonable alternative definitions would give exactly the same notion of computability.