1.) It may be possible to test multiple-universe hypothesis in the future, but not at the current moment. There are so many possibbilities in theories, how would you list them, let alone distinguish them. What happens if there are infinite universes, but no two are alike in what we take to be universal constants? What if there are only 3 universes? What if there are parrellel universes, how do w know they are infinite, and not just two. Additionally quantum mechanics could be just as easily solved by other models, which may fit the evidence just as well and with a simplier model. My point was, that scientifically, at this time, any hypothesis that involve more than one universe are , well, hypothesis, with little or no evidential backing at the moment. That isn't to say that can't change, and we shouldn't investigate them as possible, but to simply believe in them because we like the idea isn't science, its belief.
2.) I have to say that your gun theory is amusing. If I pulled the trigger 10,000 times without a shot being fired, I wouldn't assume some wierd cause, I would check to see if the gun was working. Again, you are making a arguement based on conjecture, and what-if, not based on the evidence. That isn't to say that there isn't evidence to be found, we simply haven't discovered any yet.
Additionaly, probablities don't require infinite realities to exist in order to have near infinite probabilities exist. For example, the odds are 1 to a few thousand that you will dies of a car crash, however that doesn't mean that there are 10,000 of you in existance, and in one reality, you die in a car crash. You may believe this is so, but again, at this point, it is simply personal belief.
3.) Again, just because the concept of infinite universes exists, doesnt mean the universes themselves do. It may possible to show there may be more than one universe, but it doesnt follow that there would be infinite universes. Again, without evidence and observation to back any of this, it is conjecture.