A 681

You are treated as if you had readied the weapon against a charge, at all times. This means there is no need to ready the weapon by your own action, as long as you carry the weapon.

A 681a Yes.

A 682 Yes.

The weapon uses the "wielder's" BAB and other weapon properties, including proficiencies.

A 683

Yes, a double weapon can be +1 Dancing/masterwork. Only the end with the Dancing property can attack on its own. If both ends had the Dancing property then both could attack, as a double weapon, without "wielder" action.