Well, he proved a theorem. He chose to define a “godlike object” and showed in every carefully-defined “world” such an object exists. Saying that this “proves the existence of god” is … a bit of an overreach, don’t you think?
No, I don’t. Also that’s how we prove literally anything. There is always a model, because we don’t have direct access to reality. So if your bar is that high you’re going to have to call climate change and relativity a bit of an overreach too.
A proper deductive argument that contains no errors will be valid, but it won't necessarily be sound if the premises are incorrect. In that sense deduction can most certainly be "wrong".