No, we don't have faith in any such thing. If our eyes tell us something that doesn't jibe with what we already know, we test it by other means. If you saw a bar of lead floating in water, you wouldn't think, "Oh, I guess lead floats after all." You'd test by other means. We subject things to tests all the time. If they behave in a consistent manner we decide that that is what can be expected of them. But there's no faith involved, there is a constant testing and re-testing.
2) Actually, we never imagine infinite. We can right symbols that to us mean "really big number." But no, we cannot actually grasp infinite.
Well, "imagine" and "grasp" aren't the same thing.
3) The Law of Identity is not a law, it is a philosophical criterion. Interestingly, the "law" itself falls before its own assumptions; it cannot explain anything metaphysical.
Can you give me an example?