I was talking about the expansion of the universe that is still ongoing.
Inflation has observational data already, the radiation you mention, and much of the work done with particle accelerators is to recreate the conditions of these kinds of events. This is enough to make it science, even if completely wrong.
I thought of perhaps a simpler way to put this. The realm of science is the observable universe. We can use that to develop theories of events in our universe we can't observe, as there are still remnants in the observable universe. We can't develop theories of things that never happened in the observable universe though.
Maybe someday someone will develop some method to observe effects that would show evidence of a multiverse. It hasn't happened, and personally it seems unlikely.
No we don't - I assume you're thinking of dark energy, which is a separate and (as far as we know) unrelated phenomenon. The evidence for inflation is basically "the cosmic microwave background looks like it was produced by the universe behaving in such-and-such a way"; it had no effects except for very shortly after the big bang, so we can't use it make predictions about the future and observe whether they happen or not. (We can, and have, made "predictions" about things that haven't yet been measured, e.g. inflation was used to predict what the CMB polarisation would be before we launched Planck to measure it - but what we're measuring is something that happened in the very early universe).
So I don't see a lot of difference between that and e.g. a theory that says (with evidence) that our universe is the result of a symmetry-breaking process that would naturally have produced an ensemble of similar universes.