for variance, you would have to divide by „entry“ or the number of events in your run, or some other value, depending on what specific statistics you are interested in (for this, one has to know what is going on in the individual simulation setup very thoroughly)
fyi: for your second initial question: Creating a spherical-shell detector - #5 by JDecunha
maybe you can simply attach a primitive scorer
/score/create/realWorldLogVol sphericalscoring_shell
/score/quantity/doseDeposit dose
/score/close
to the approach described there?
otherwise: interpolating a carthesian grid to polar has been done once or twice before (e.g. Spherical interpolation in Matlab from Cartesian Grid - Stack Overflow)