You could call this science worship, I think. There is also the word "scientism", meaning a sort of extreme and exaggerated regard for science, so maybe "scientism" is the best fit for what you describe. You add in the idea of sacrificing human beings for science, and this already has a name: murder. Murder is wrongful intentional unlawful killing, and that is what you are describing. It was common under fascism of course.

When you say that science can or cannot explain this or that what you ought to mean is that, at the bare minimum, the proposition that this or that happens can be deduced from some other more general proposition or propositions. So it is not unreasonable to think that there isn't anything science can't explain. Maybe there are infinitely many propositions, and they are all related deductively. Here I am just applying the nomological-deductive model of explanation, but the same point could be made using any other model, in its terms. It also seems to me that your question confuses two senses of "explain", one in which why a stone falls to the ground is explained when we deduce it from a proposition about gravitation, and another one, in which explanation is ultimate and absolute rather than relative to other propositions, and in which we cannot explain why the laws of nature are what they are and why they exist at all. If you stipulate that the second sense of explanation is legitimate, then your problem...

Is the idea of backwards causation coherent? It seems not, as you could, for example, cause earlier events, such as your own birth, not to have happened. There is also the famous "bilking" (cheating) argument due to Max Black, according to which you can prevent the future cause of something that has already happened from occurring. All the same, philosophers, particularly Michael Dummett, have taken the idea perfectly seriously, and defended it. You write that you doubt that a scientist would take the idea seriously, but plenty of physicists, including Richard Feynman, have indeed used the idea for a variety of purposes, including the remarkable idea of positrons running backwards in time.

Right on the money! It is extremely improbable that with say four dice I shall roll four sixes (1/1296 against, if my arithmetic is right, and there are no biases.). But I have done it, with dice that otherwise showed no evidence of being biased. What does this show? Nothing at all! In particular, it does not show the existence of a dice controller who favours me - assuming more sixes are better than fewer. Suppose human life is extremely improbable. What does that show? Alas, again the answer is, absolutely nothing at all. The improbable sometimes happens, although, of course, not very often! We should thank heaven that it did!