Steven, nobody can prove that the laws of nature are immutable. We have arrived at that provisional conclusion by way of induction. Science is open to change on that point, but so far as we know, they are effectively immutable. The burden of proof is squarely on those who claim they may not. (Physicist Lee Smolin has tried to argue that they are not, but not very successfully, in my mind.)

As for causation, we need to move beyond Hume. To begin with, it is not the case that everything is causation. There are plenty of empirical correlations that are not causal (just ask any statistician). Second, we have a number of interesting theories on causation that are more advanced than Hume’s take. See this article: https://plato.stanford.edu/entries/causation-metaphysics/