What's the technical term for supercharging an acid with an oxidizer? And does it always work?
I don't know if it's called anything, but when you use an oxidizer in solution, you usually need a source of hydrogen ions for the oxidized oxygen to be reduced.  In the case of hydrogen peroxide, $\ce{H2O2}$, the oxygen is in the $-1$ state rather than the normal $-2$.  The usual way $\ce{H2O2}$ acts as an oxidizer is to be reduced to water in the presence of 2 hydrogen ions, usually from a strong acid:

$\ce{2H+ + 2e- + H2O2 -&gt; 2H2O}$

Notice that the reaction consumes 2 electrons on the left, which would come from other reactants that have been oxidized (i.e. lost electrons).

The point is that a strong acid by itself has only a corrosive effect, and a highly dehydrating effect in the case of sulfuric acid.  But if you add an oxidizer, then in the presence of a fuel (like an organic compound) plus sufficient energy (say from the heat of reaction), then you are effectively getting a combustion reaction as well.  This is the sort of "combustion" that goes on inside your body to use food as fuel, for example.  I supposed this could be called "supercharged".

EDIT: So to answer your specific questions:

1) No technical term that I know of;

2) Yes, assuming the acid is strong enough to donate protons;

3) In most organic molecules, carbon is more electronegative than hydrogen, so it can be oxidized by oxygen.  And so you get a "combustion" reaction where molecular carbon is oxidized to elemental carbon (i.e. burnt).