When Schrodinger proposed his thought experiment, he was not suggesting that the cat would end up "both dead and alive" (which is a somewhat misleading way of describing superposition - you'll find it in pop-sci treatments of quantum mechanics, but not in serious textbooks). He was pointing out a problem in the then-current (~1930) understanding of quantum mechanics: everyone knew perfectly well that the cat would be either dead or alive and not in this weird superposition, but the math didn't seem to predict that outcome.
This problem was solved over the next few decades with the discovery of decoherence - google for "quantum decoherence" or give David Lindley's book "Where does the weirdness go?" a try. It turns out that the same Schrodinger's equation that leads to superpositions of subatomic particles predicts that larger systems composed of enormous numbers of interacting particles (like a speck of dust, or a bacteriurm, or a cat, ...) will behave classically; this is loosely analogous to the way that the ideal gas law and thermodynamics emerge when you apply Newton's laws to a system made up of a large number of molecules.
So:
1) Yes, the equation works for everything regardless of size. However, just as the behavior of a large volume of gas is very different than the behavior of a single gas molecule bouncing around in an otherwise empty box, the end result of applying the equation in different situations can be very different.
2) It is, obviously, impossible to disprove the proposition that "the universe is just a creation of us and our perception". However, there is nothing in quantum mechanics, Schrodinger's cat, or the double-slit experiment that gives us any reason to accept that proposition either. Based on our current understanding of the math behind quantum mechanics, there's no reason to doubt that the universe was out there and obeying the laws of physics long before there were any conscious beings to imagine it into existence, and it will still be out there long after we're gone.