I don't remember the beginning premise of Shaun of the Dead, but rabid positive thinkers reentering society sounds about right.

No it would not be necessary. A control group would give you confidence that it wasn’t some other aspect of the experiment that resulted in people surviving. But we have strong enough priors on rabies that we should feel confident the probability of accidentally curing rabies with a different aspect of the experiment is extremely small.

If that were the case we could do a later experiment to establish that factor. “We’re doing ‘something’ that makes people survive” is good enough for a first attempt.

No, and must likely the ethical committee review would reject the use of a placebo group in the study.