Actually not true. If you take scientific theory like quantum mechanics, as an example, you find that the theory can be used to explain many phenomena. This particular theory explains everything from the structure of atoms to electricity, to nuclear fusion, etc. etc. But it relies on mathematical structures and equations that are themselves unverifiable (waves of probability described by imaginary numbers which cannot be actually directly shown to exist by any conceivable experiement). Yet scientists agree that it's good solid science (though its basis is unprovable), because it has explanatory power. The same with my religion, Christianity. Christ provides, for me (obviously not for you), deep answers to many of the questions that mankind has always had. Many of those answers provide a theory that explains quite well (for me) many of the human phenonema that I observe.
This is not correct. In the orthodox interpretation reality is ascribed only to the measurements - the mathematical structures and equations (read quantum states) are for computational purposes only and no reality is necessarily implied.
Well, (Do not try this at home) if you stick your tongue in a light socket, the part that stops your heart is the real part; the imaginary part knocks your teeth out.