How do weapon properties apply to double weapons?

Question

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.

Answer 1

Yes and No. Intrinsic Weapon properties only apply to the end that they apply to and do not apply to the other end. Magic properties apply to both ends of a weapon equally.

This is a change from the original rules printed in the Adventurer's Vault. The updated double weapons table and double weapons rules can be found in the file UpdateAV1.pdf from the Official D&D Errata & Rules Updates page, or in the online compendium.

The description you are referring to with the double sword is flavor only and the stats of the double sword are to be used regardless of the flavor. In fact, in the case of a double sword, both ends are now off-hand light blades. The damage dice are those given for each end, in this case a d6 for each end. The main hand of the weapon gives you a defensive bonus of +1 to AC.

If you want to see a double weapon that is crazy different on each end, the Urgrosh and Kusari-gama are good examples.