Yes, the interesting deal with mathematics from my perspective is that we are capable of finding nice "islands" of truth that serve us well. Almost all mathematical theorems are basically useless to us (for example the conjunction of any theorem with another theorem is a theorem, but it is trivial), and the tricky part of math is in determining the right area to explore. The fact that we can find interesting/beautiful theorems etc. is most likely because they are easily compressed w.r.t. our environment. My personal view is that the right mathematics we should be in pursuit of is the facts that help to serve God's plan and give him glory. I am not very good at math though, lol, despite having a bit of basic knowledge.

Short note again: mathematical theories are simply the logical result of some set of axioms, and a non-trivial set of axioms can't admit a proof of self-consistency. I think that I understand what you are saying, but it is important to be pedantic about these particular points imo.

Funny, I think that it is technically correct that God requires nothing from us, however it could be a bit misleading. A succinct version of my view is that there is one group of people or animals that exist because they minimize some cost function, e.g. they are particularly well adapted to their environment. However, then there are the children of God who exist as a direct logical consequence of God's existence and their faith. It is possible to be in both categories or in only one, but those who find themselves in the latter category are somehow more permanent and exist, I guess, in a 'fuller' way. So God could decide that we are in the latter category despite a lack of faith, but my best guess is that he just doesn't, so it is kind of sort of implied that he requires us to have faith. I think he probably leaves uncertainty about this question on purpose.