Why Is Anybody Convinced There Is A God?

Proof implies that something can't be wrong.  If we've proved that P, then it's not possible that not-P.  Otherwise we haven't proved that P.  Proof also has a normative implication. 

One's support for something is simply the reasons that one believes what one does.  And it doesn't necessarily have a normative implication, because the reasons that one believes what one does can be very personal.

Re different people experiencing different things, that's simply because we don't have identical perspectives.  It doesn't imply that anything is illusory.  We don't occupy the same space, for example, so you perceive things from one perspective, and I perceive them from another.  That's not the only thing that's going on there, but it's one example. 

So if we both walk into my kitchen, we should both see the refrigerator.  We won't see it exactly the same, because we don't have identical perspectives--we're seeing it from different angles, we might be seeing different sides, etc., and we don't have identical perceptual faculties  If you don't see it at all, then there's reason to wonder what's going on with your perceptual faculties, or what might be going in your brain aside from your perceptual faculties, once you receive that external information.

"Purposes" are simply things we invent for ourselves as individuals, when we do (not everyone invents a purpose for him/herself).