The mechanics of wielding a double weapon is described in the Adventurer's Vault on page 10:
Wielding a double weapon is like wielding a weapon in each hand. The first die given in the damage column of the table for a double weapon is for the primary (or main) end of the weapon; the second damage die is for the secondary (or off-hand) end.
Does this mean that the off-hand property is only bestowed upon the the secondary head?
The double axe, double flail and double sword all have the same damage on both ends and furthermore they're illustrated as being symmetric. As there is no particular way to separate the ends apart, Shouldn't this mean that the off-hand property applies to do both ends equally? Not unlike how a shortsword wielded in the main hand still retains the off-hand property.
My main question:
Q.Main: Is it true that a weapon property or weapon group classifier always apply on both ends simultaneously?
One reason for why this is unclear to me is given by the following example: The double sword has the light blade and a heavy blade property, yet both ends are described as longswords:
Double Sword: This well-balanced weapon combines the deadliness of two longswords with increased defensive capability.
Longswords only have the heavy blade property. This leads me to think that the weapon descriptions are more akin to fluff whereas the table with weapon group classifiers and weapon properties are the crunchy matter.