Can all laws of physics derived by a single or lists of more general laws? I have always been curious about deriving thousands of laws from more general ones.
Can general laws or models of physics explain minor concepts completely? 
For instance, can Standard Model explain, well, $F=ma$?
 A: In general, it is possible to derive "minor" concepts from a more general theoretical framework. This is the very definition of deductive reasoning, and it is in fact at the foundation of the scientific method. However, there are cases where the hierarchy of concepts is not so clear, in the sense that it is not always straightforward to decide which is the "minor" and which is the "major" concept from which the former derives.
Specifically, it is possible to derive classical mechanics as a macroscopic limit of quantum mechanics (which is, by the way, the general language in which the standard model is written). In particular the result $F=m a$ can be derived form the Schrödinger equation, and this derivation is known as the Ehrenfest theorem. It states that 
$$
m\frac{d}{dt}\langle x\rangle = \langle p\rangle,\\ \frac{d}{dt}\langle p\rangle =  -\left\langle \frac{\partial V(x)}{\partial x}\right\rangle,
$$
where $\langle x\rangle$, $\langle p\rangle$ are the expectation values of the position and momentum, and $V$ is the energy potential of the force, $F=-\left\langle\frac{\partial V(x)}{\partial x}\right\rangle$. In very simple words and loosely speaking, the Ehrenfest theorem states that, in average, quantum mechanics follow classical mechanics. 
I said in the beginning that in some cases the hierarchy of "minor" and "major" concepts is not evident. For example, one can consider thermodynamics. Most of the concepts of thermodynamics can be derived from statistical mechanics. Now, statistical mechanics comes in two main flavours, based on classical and quantum mechanics respectively. One can derive the fundamental concepts of thermodynamics either from quantum statistical mechanics, or from classical statistical mechanics. In this case, although thermodynamics can be derived in some way from quantum or classical mechanics ultimately, it is clear that in a certain sense thermodynamics is more general than these, and that the most important results of thermodynamics (e.g., 1st and 2nd principles) are largely independent on the microscopic details of the physical description.
A: Physics is a science that is extending more and more. The most general unified theory is String theory. It contains the Standard model and gravity. However, there are no proofs about the theory. Maybe it can contain errors. Even string theory has a lot of assumptions: Strings and branes that must exist, many geometrical things about the interactions between these, extra dimensions, supersymmetry and much more.
Physics is changing during the human history. Maybe in near future might be disproven very basic things like energy conservation or the understanding of gravity is quite different.
Nature doesn't behave that simple as we think. 
A: The way it works is that any given physical model is an approximation, and has its limits.
The current edge of physics is where we no longer see variations between the model and what we see in nature.
For example, no one seriously contends the flat-earth model E2H (euclidean ground + height), but the flat-earth physics is pretty much all you need to build houses, cities and so forth.  
For long distance navigation, we use a model S2H, which means we use spherical geometry and height to make the world.  You can replace the mathematics of E2H for S2H, but it's a lot of work for no appreciable fix.  Geodetics use Se2H, which replaces the sphere with an ellipsoid.
Likewise Newtonian physics E3T = euclidean space and a separate time axis, is good enough for poking tin cans around the solar system, and is the approximation that SRT = E3J gives, when $c = \infty$.  But one notes that the space agencies do well without having to implement special relativity E3J.
Of course, you would get exact values when you start dealing with things in E3J, but you have to do things like consider all sorts of devils on the way, such that chemical energy is stored as mass, and that E3J -> E3T and S2H -> E2H, and that ordinary schoolbook geometry is good enough for most problems.
Then of course, where E3J departs from reality far enough to be noticed (ie an anomaly), then you invent some new theory, say GEM or GRT to explain these differences.  This is the limit of our research, and this may be superceded by a new model, say XYZ.
