There is measurable evidence on the quantum level, the issue is finding a way to measure in the macro level. And, yes, once we can, it may falsify the multiverse hypothesis.

That depends on which kind of multiverse you're talking about. If we go with the quantum, then the multiverse comes about as a logical result of our observations of the behavior of subatomic particles and their ability to be in two or more different, contradictory states at the same time (such as being in two different places at the same time). Since the particles can occupy contradictory states at the same time, so too must the things they make up, like us and the universe. Since we don't see this constant variance in our observations of reality, one solution is the quantum multiverse hypothesis, allowing the variances by postulating divergent universes.

As for the infinite energy requirement, one of the possible solutions is that the calculated energy of our universe is zero. Everything balances out, so our universe's total energy is zero. And yes, you can get more zero states from a zero state.

True, as of right now the multiverse hypothesis is unfalsefiable, but that also used to apply to the theories of gravity, germs, electromagnetism, organic chemistry, cells, the speed of light, photons, evolution, all of them. As we develop that may change.