Do miracles break natural laws, such as the laws of gravity or entropy or the lay-level biological law that dead things stay dead?
No, miracles do not in any way break natural laws. Here’s how.
The laws of nature are not prescriptive–like moral laws. Gravity does not suggest how things should be, rather it’s a term referring to something that is either found true of nature or it is not. Gravity is never broken, at least, not without intruding upon it from outside an otherwise ‘closed system.’ If we are talking about a vaccuum-sealed, airless room, that would be a literal closed system. And in that room, a bowling ball and a feather are suspended on a platform. Pull that platform away and the bowling ball and feather are naturally affected by gravity, having the same force, pulling them the same speed, at the same time, bringing them to the ground simultaneously. That is a good old-fashioned lab experiment, closing the system so that extraneous influences and effects can be minimized. Would a puff of air into the vacuum “break” the law of gravity? Not at all, it would just be an intrusion upon that closed system. If the door were left open, or the feather were tied to a rafter above the ceiling, or powerful magnetic fields were beamed in there from a machine outside the one-way glass walls–all of these would intrude on the “closed” aspect of that system.
Now the laws of nature such as Newtonian forces, quantum principles, einsteinian theory, biological inferences (evolution, mating patterns, etc.) describe observed patterns of nature that are reliable so long as the system in question remains closed.
But what if you open the top of the box, exposing the system? Well that’s what miracles are and the laws of nature are no longer describing that system. It does not “break” the laws of nature since they only describing closed systems, not open systems.
One has full liberty to believe that miracles don’t happen, but it does no good to point out the regularity of nature, or describe natural laws since theists have every reason to believe that nature operates in regular reliable and lawful patterns. But there is nothing in nature that demands there only be a nature, only this system, closed, with nothing outside it. Science never even spoke to the brute possibility/plausibility/intelligibility of a supernature. But this metaphysical naturalism and its remarkably hard to prove. Usually, the metaphysical naturalist does not even attempt to prove naturalism but rather assumes it and demands that the theist shoulder the whole burden of proof. Nevermind that naturalism is the stark minority position, never mind that there are thousands if not millions of miracle claims, never mind that closed systems themselves require an explanation, never mind that nothing of nature is known to be able to cause itself–not the parts of nature, much less the whole of nature). Instead, by demanding that theists give (natural law) scientific proof of miracles, or a material and natural demonstration of an immaterial and supernatural ‘god,’ the naturalist merely points out that the claim of supernaturalism is different from naturalism, that ‘god’is not non-God, and that if God exists he/she/it would not be nature (or, given pantheism, would be indistinguishable from nature). These are trivial claims.
How then can we solve this ideological impasse? First, we should be clear that there may be natural evidence consistent with a miracle claim, even if supernatural causes cannot–by the nature of things–be directly observed as a natural cause. Second, we should grant that it’s hopelessly circular to define nature as “all that exists.” This is merely defining nature as naturalism, and if there were a supernatural God then he would have to also be natural if he could exist at all; thus nature and supernature are the same, and the terms dissolve into meaninglessness. Third, we must allow that inferences can be made from effect to cause–even if the cause is only slightly known through its effects. People may dispute which of these inferences are sound, but its categorically stultifying to deny that that inference can ever be made coherently. For example, we can infer a killer by his modus operandi, or an Apple product by its logo, or an intelligent designer by (apparently) designed effects. These are partial and imperfect, but still probabilistically valid. Fourth, we must allow that scientific demonstrations are not the only means to truth, knowledge, or inference. I won’t belabor this point but suffice it to say that to assume otherwise is to commit the manifestly discredited assumption of scientism where “science is the only means of knowledge [not counting that very statement which is not itself a scientific product but a philosophical/theological conclusion].”
For more on this subject see the work by Alvin Plantinga, “Where the Conflict Really Lies”
Intelligent Christian Faith 
I would agree that science isn’t the only way to know things. Science is a very high standard. We can also learn from simple observation and induction, this is less reliable than science, but more reliable than, intuition say, or wishful thinking. We should also be very careful of is conclusions from ignorance.
To continue your vacuum analogy, an observer from within the room who might conclude “all things fall at the same rate”. This is a perfectly logical conclusion based on observation and induction. But one day the feather falls slower. She would be wrong to conclude that a “supernatural” force had intervened. If she could detect air, she should try. She could then expand her theory to the more accurate “all things fall at the same rate in an vacuum”. But let’s say she cannot detect air, or that air detection technology is 100 years away. She would still be wrong in concluding the change in the phenomena is supernatural, but of course she would be wrong in reaching any conclusion until she had evidence for it. The right thing to do, is say this is “unknown” and keep looking. It is an argument from ignorance to reach conclusions when we have no evidence.
I also see nothing wrong with equating “all that exists” with the natural worlld. It is a shorthand. I’d be happy to use another shorthand if you have one.
Why are you forbidding the possibility of causal forces outside of this system? That seems a bit dogmatic.
You suggested, for example, a case where she cannot detect air and would be justified in believing that bowling balls and feathers fall at a different rate of speed. I don’t see how that analogizes with the possibility of God/supernatural causal force unless you are dismissing out of hand how billions of people have already detected God (or claimed as much), thousands of miracle and prophecy claims are still standing, and multitudes have proceeded to order their lives around that fact, and to account for the rest of reality accordingly. We can use natural science to account, pretty well, for descriptions of the mechanisms and materials of the physical world. But reality also includes the observed abilities of cognition, perception, intentionality, language, free-will, moral knowledge, moral guilt, objective goodness, love, personhood, human nature, design in the world, beauty, apparent meaningfulness to life. God-belief has proven remarkably cogent and effective in explaining this wide array of data points, even if the methods of natural science don’t suit supernatural objects very well.
Forbidding consideration of possible supernatural causes seems dogmatic and unwarranted. Bear in mind, I’m not suggesting some hasty assumption that if a feather falls slower than a bowling ball we assume God holds it up–maybe he likes feathers better and keeps them closer to heaven. Theologians even know that we should understand our world and its natural order and we don’t need to appeal to a supernatural mind to account for how mechanics work. We just need a mind to understand why they work or perhaps, how they got here in the first place. These would be areas where miracles might be necessary just to account for observed nature.
Sorry, I thought I was just using your analogy of the vacuum room etc. I thought you were using that analogy to show a closed system, the vacuum room, can be affected by forces outside that system. I thought your analogy was that our universe is like the room, something otherwise miraculous in that system, the feather falling slower, might seem miraculous if you do know about air. You don’t realize that there is something outside the closed system. My point is simply that what you described is not analogous to the point you are making, but rather the point you think you are defeating. It wasn’t a closed system with its own laws of nature, being affected by something outside the system with different laws or something. Rather the observer, thinking the change supernatural, perhaps for good reasons, wrongly apprehended the scale and complexity of the system. It would be unfortunate if the observer in the room were to accept on ignorance that it was a deity, or also that it was some undetectable mixture of gases. One is right, one is wrong, but until it is observable, it is a mistake to conclude without evidence.
I am not forbidding anything. But I will not accept supernatural guesses as explanations for unexplained phenomena anymore than I would accept natural guesses. My cynicism towards supernatural is because no explained phenomena has ever been explained by supernatural causes. Not lightning, not disease, nothing. We are left with Jesus on toast and tales from thousands of years ago.
Take the example of crop circles. For a long time these were unexplained. One cause might have been a deity attempting to communicate with humans, by supernatural unknown means, “outside the system” in violation of natural laws. Another would be aliens using unknown means by way of expanded understanding of natural laws unknown to humans. Another is that it is humans doing it by unknown means consistent with our understanding of natural laws. In this circumstance what is the reasonable conclusion? Before we had more information, the best answer was “we don’t know”. But even arguing from ignorance, aliens makes more sense than deities as this does not require violations of natural laws. Turns out that it was humans.
I don’t deny our picture of all-that-exists-on-any-scale may be woefully ignorant. A deity may exist that may use mechanisms that we cannot imagine or hope to understand. But if that is the case, THAT is the all-that-exists-on-any-scale in which we inhabit.
All I am saying is let us put ourselves in the Incas position and not assume that the newcomers with unexplained powers are gods and give them all our gold, they might be spaniards.