In fact, none of the three theories is equipped to describe the gravitational effect at very small distances. Our descriptions of the very small and of the very complex don't include gravity, and our theory of gravity breaks down at short distances. If we wish to discover what happens inside black holes, or what happened at the start of the universe we need a new theory that joins the very small and the force of gravity.
This is an example of something that is described by my second thought which is that these areas are not distinct. We can easily imagine complex situations in which gravity acts on very small scales. This idea leads to the main motivation for the search of a theory of everything: if we have distinct theories, where does one cease to apply and another take over? And perhaps more importantly, why? It is certainly possible to imagine a universe where the laws of nature are not the same everywhere, but one in which the laws change not based on location, but on the number, size and separation of entities involved in a particular interaction seems awfully bizarre.
Mathematics is not a description of reality. Mathematics involves setting rules and seeing where they lead. The rules do not have to have anything to do with reality all. Often, and in mainstream mathematics, they are based on "truths" that we observe. But that does not mean that they do actually represent that reality. We started by study Euclidean geometry based on the idea that space is flat, but it turns out that it isn't. We never have (and never will) prove the existence of a quantity $\pi$ partly because we are limited in the accuracy of our measurements, but more importantly because we don't know whether time and space are discrete or continuous. If they are discrete, the quanta are sufficiently small that the continuous model of the real numbers is (thus far) are reasonable approximation, but that doesn't mean that it is exact.
The idea that we could ever work out deterministic equations for the universe seems inherently unlikely to me. Quantum theory is probabilistic, not deterministic. And even if it weren't, we know that we can't measure both the position and velocity of any particle - and we must be talking about particles at the start of the universe because of the small size of the universe at that point. We know already that there have been a lot of lucky breaks in the development of life on this planet. There are countless extinction events that could have extinguished it, and even some events that have happened only once in the history of the planet without which advanced life forms could not have formed. But even if we didn't, the apparent scarcity of life we have observed in the universe would tell us that. However, more or less every stage of the development of life has some widely accepted theory attached to it.
In The Blind Watchmaker Richard Dawkins talks about how the theory of evolution can be applied to non-living scenarios to account for the local accumulation of chemicals that would eventually combine to form life. He mentions lab experiments in which the building blocks of life have "spontaneously" appeared in test tubes of suitable organic compounds. In essence, there are reasons to believe both sides of the argument: that life (of some sort) is inevitable given the appropriate "initial conditions" that eventually manifested themselves on earth; but also that those initial conditions were rather a fluke and that subsequent events might easily have terminated the development of life.
I'm not an expert on Complexity theory at all, but my reading of chaos theory is not that it tells us how things happen. Instead, it relates how, although tiny variations in initial conditions might create huge differences in later results, there are still overarching principals that apply whatever those initial conditions may have been. These principals are seen more as describing results than causes. I would expect that such results have causes that are described by other branches of science, notably physics.
Your claim that "physics is set and unchanging but nature is flexible so we need a description that reflects this" is somewhat baffling to me. Physical theories change all the time as the result of research. There is also some possibility that some of the laws of nature have also changed (although not since the very early universe). But even if you refer to the "unchanging" laws of physic that science is trying to uncover, it still makes little sense. We have very, very simple games (cellular automata) such as Conways Game of Life that prove that extremely complex results can emerge from even the simplest unchanging rules. Why the laws of physics should be any different, I don't understand.