Why is magic acid a superacid? The above is a representation of magic acid. The left part is the acid; the right part is the solvent. Why would this combination make for a particularly good acid?

The left part looks like a sulfuric acid derivative, except one of the oxygens has been replaced by an electronegative fluorine. Why can't we replace all the oxygens with fluorines? Wouldn't that make for an even stronger acid through inductive stabilization of negative charge after proton loss? 

Also, does the solvent play a role in magic acid's acidity? Does the highly partially positive Sb central atom play a role in stabilizing negative charge on the solute after the solute has been deprotonated?
The explanation is that sufficiently strong Lewis acids like $\ce{SbF5}$ will form adducts even with very weak, traditionally non-coordinating Lewis bases like $\ce{SO3F-}$. The resulting anionic complexes are extremely stable, with the negative charge distributed over a large, highly polarizable molecule and inductively stabilized by the fluorine atoms. The formation of this complex, in turn, promotes the autoprotolysis equilibrium:

$$\ce{HSO3F + HSO3F &lt;=&gt; SO3F- + H2SO3F+}$$

The protonated species above is the most active molecule in sufficiently concentrated solutions. (In reality, the composition of these mixtures may be much more complex, with dimers of the form $\ce{Sb2F10(SO3F)-}$ and possibly more complex oligomeric structures. See, for example, this book.)

While there are some more recent and exotic examples of such Brønsted/Lewis acid mixtures, the idea is actually a fairly old one. Perhaps the most common example: sulfur trioxide in sulfuric acid gives a solution known as oleum, which contains a proportion of disulfuric acid molecules. The resulting mixture is considerably more acidic than pure sulfuric acid alone and has various uses in industrial applications as well as laboratory-scale synthetic organic chemistry.

As for why the oxygens cannot be subsituted with fluorines to yield an even stronger acid system, I can only give a speculative answer. It seems to me that a hypothetical molecule such as, e.g., $\ce{SF3OH}$ (if this is what you're imagining) would probably be very liable to decompose:

$$\ce{SF3OH -&gt; SOF2 + HF}$$

In any case, I can find absolutely no relevant literature, which in and of itself says something about the stability of such a molecule (or perhaps my ineptitude, as the case may be).