Energy stored in electric field and work done to change a charge configuration I had read a problem where a point charge is placed at the center of a thin grounded conducting shell. The energy for removing the shell off to infinity was asked. It was calculated by using the following expression for energy stored in the electric field, before and after, and subtracting them.

Is the energy in some charge configuration only stored in the electric field? For example, is the energy required to move one positive charge in the presence of another given by the difference in the energy stored in the field before and after?
 A: 
Is the energy in some charge configuration only stored in the electric field? For example, is the energy required to move one positive charge in the presence of another given by the difference in the energy stored in the field before and after?

Yes and no.
We do have to define electromagnetic energy as the energy of the fields, not, as in Newtonian mechanics, in terms of potential energies that depend on the instantaneous positions of particles relative to other particles. If we tried the Newtonian approach for E&M, it would fail because we have radiation.
However, it's easy to come up with examples where calculating the energy in the fields doesn't actually work either. For example, suppose we put a point charge in a uniform field. Then we have two problems: (1) The energy is infinite. (2) By translational symmetry, the energy can't depend on the charge's position.
Difficulties of type #1 can be approached as follows. Let object 1 have electric field $\textbf{E}_1$ and let there be some other electric field $\textbf{E}_0$, which we can say without too much loss of generality is fixed. Then the total energy depends on $\int (\textbf{E}_0+\textbf{E}_1)^2 dv$, but if we only care about the dependence on how object 1 is translated or rotated, then we can just calculate the part that varies, which is $\int 2\textbf{E}_0\cdot\textbf{E}_1 dv$. If we take the point charge to be the limiting case of a sphere with radius $r\rightarrow0$, then this interaction energy converges in that limit.
Sometimes a trick that works for issues of type #2 is to artificially introduce a boundary, e.g., make the uniform field be created by a parallel plate capacitor of finite thickness.
A: It is true that the energy stored in a given system of charges is stored in its electric field.  
However, it is difficult to calculate the work done in moving one positive charge in the presence of another in terms of difference in energy stored in the electric field, as the electric field energy of a point charge diverges as we approach it. 
