Q. Do we need a minyan for the reading of the M’gillah?
This should ideally be in the presence of an assembly of ten, not because the M’gillah needs a minyan but in order to publicise the miracle (“In the multitude of people is the King’s honour” – Prov. 14:28).
This quorum is not the same as the minyan that is needed for, e.g., K’dushah or Kaddish. Nor, according to some views, do the ten who make up the M’gillah quorum all have to be males.