We've got a bit of a language problem here that's interfering with logic. You need to define your terms strictly, then stick to them. Absent that, you get what logicians call a "shifting middle term" or "fallacy of amphiboly," and end up thinking things that just aren't true.
I said that you are claiming that conventional Christians believe that faith requires a proof. You are now saying that there is no such thing as proofs.
You need to use terms consistently, or you will confuse your argument.
No, I've been speaking of "evidence." In contrast, you've been speaking of "proofs." The two are not at all the same: evidence is probabilistic, and proofs are definite. You're making a category error there.
To clarify, there's no "proof" for anything inductive...only evidences that increase the likelihood of one thing being true or another being true. Faith requires evidence, and evidence is what is necessary for warranted belief in real life situations; but proof --a formal demonstration of accuracy -- is only available in maths and formal logic, and only then because they are self-refererential systems.
Clearer now?
Faith=trust? How can I trust you if I do not have faith that you exist?
Clear up your terms again, and your confusion will dissipate. You're now using "faith" as an equivalent for "belief," which would be correct; except before you were using it as a synonym for belief-without-proof, which is an incorrect definition, as you have seen. Let me suggest you stick with that new definition.
But then, your second question has already been answered.