1- How do you treat AOE situations? Keep going single target? Drop dots on multiple targets? Anything fancier than Katon - Kassastu - Doton?
For AoE, I personally rely on Doton if we're camped, otherwise, I'm spamming Katon due to the tank constantly moving the mobs off the Doton puddle. If there's three or so mobs, I Mutilate and Shadowfang each mob, then work my or each mob individually.

2- Is it really bad in using Duality on Armor Crush rather than Aeolian Edge if your Huton is low when Duality comes off cooldown?
There's no rule to say that you CAN'T use Duality on Armor Crush, but I'm against it unless I popped Duality after realizing Huton is under 5 seconds. You won't get 60 seconds of Huton, though; only a harder-hitting Armor Crush, and that's IF you did it from the mob's side.

3- What can a NIN do specifically to speed up dungeon runs in terms of killing speed with adds?
Refer to my comment for Number 1. I use that just like I do it on my BRD. On BRD, I use both "Bites" on each mob, then apply Iron Jaws to each mob, then begin burning down the mobs. So for NIN, again, see my comment for Number 1.

4- What other masteries of the job have you come across you'd like to share?
I'm NIN main, but am no master. My NIN doesn't even parse high, but she's definitely not a handicap within a group. To be honest, I'm considering moving away from NIN, as she causes fatigue. I'm pressing my buttons harder and faster with the mentality that I will push more dps that way; it wears me out eventually. If I miss the chance to reapply Armor Crush because I'm trying to push damage, I just lost damage, because I'm now attacking slow, and that Mudra could have been used for Raiton or Suiton instead of Huton. Also, I play solo. People I know all play with their groups, so I have to rely on Duty Finder. With that, I'm not able to enter content at a decent rate since DPS queues are long. I'm slow transitioning over to be a tank main, notably DRK.