Parry only lets you forgo 1 attack, so you wouldn't be able to drop both off-hand attacks to gain 2 parries.
I asked James Jacobs a similar question about TWF and a Duelist's Precise Strike, and he said you wouldn't get PS damage since you're still using a weapon in your other hand (though he's decidedly not the "rules guy" and I still disagree with his position). I later posted my question on the Rules Questions board for people to discuss (I posted it late and kind of forgot about it until after the discussion had faded, so that's why I didn't comment in the thread). Note, I asked these questions before realizing Parry only lets you drop a single attack.
I'm not sure why a Duelist would want to use (Improved) Two-Weapon Feint, unless you have rogue levels and can't get SA otherwise. You could Main-Hand the dagger, but you'd suffer heavier TWF penalties.
Is disarm maneuver considered an attack?
Yes, all combat maneuvers are attacks.