Mathematics is about logical patterns. A world in which you can be mistaken about such fundamentals as the value of 2 + 2 is not a world where you can put any trust in your logical deductions. As such, if you ever do notice such a slip, I suggest that the cause is likely to be something deeply wrong with you, yourself, and not that you are living in a computer simulation.
The test of any religion is whether cultures believing it tend to thrive and improve the quality of their lives or not. The whole point of the word of God is that following it gives you...
Yes they do. If the world is controlled by an intelligent entity, then statistical proofs tell you about the behaviour of that entity, rather than impersonal laws of physics, but they still tell you what's likely to happen.