Haha, whatever you need to tell yourself I guess? It's not that axioms aren't questioned, anyone can say "A can totally be non A", but it can't actually be shown false. Just when you question "the self exists", you must exist to ask the question in the first place. I think it's probably a new low for a materialist to rely on the idea that axioms are "faith... what you want to believe as true". Hell materialism and science rely on such axioms, so are those just faith as well? If something is not an axiom then it's easy to show that, so why have you not even tried? Instead of this childish crap, why no show how self existence is no self evident, necessary, relies on premises, or can be argued against without it still being required to be true.
Your other ridiculous examples of axioms show you clearly don't understand the concept, so hopefully that simplifies it enough.