Wrong. Science requires faith in quite a few unprovable axioms, right at its core.
True, but that doesn't require faith. We can accept propositions provisionally if they are useful. We have mountains of technology that could only have been created by presuming the scientific method works. We have zero technology that could only have been created by faith.
Identity, that things are what they are, and are so consistently, being one.
If things aren't what they are(whatever that means), it does not affect the outcome of our experiments or the models we come up with to explain those results.
No science proceeds without starting with hypotheses, the plausibility of such ultimately being true being supported, at that point, only by the equivalent of faith.
Hypotheses are testable, and they are discarded when they fail tests. That's not equivalent to faith at all.
To avoid the common misrepresentation, "faith" does not mean "belief without evidence", that's simply an intentionally-false statement of what theists mean by it, made by atheists, to fit a pre-built argument. "Confidence in the face of incomplete information" is an accurate rendering of what theists actually mean.
I don't see a difference. If you're claiming that "incomplete information" is greater than "zero information", I'd like to see some of that information that leads you to be confidant about the existence of anything supernatural. I've never seen any.
Either "rock is good" or "rock is not good" is a factual claim. One or the other is true, neither is provable.
The problem with that is that "good" is not well defined. Propositional logic does not apply to squishy english terms. Av~A doesn't work when A means different things to different people.
A better example concerning unprovably true statements would be Godel's theorems. But that still doesn't help your argument. That unprovable statements exist does not imply that they are all worth consideration. Hell, we don't even have the time to evaluate all the potentially (dis)provable statements.
"The theist" can certainly hold the position that his belief is one of opinion, rather than fact.
You can have an opinion about a factual claim, but that doesn't make the claim non-factual. You're free to have whatever opinions you want, but your opinion about objective reality is worth nothing if it is not supported by evidence.