1.) DA/Berserk for Cat 1. Cat 2 is less of a given. Warrior's Charge is nice, and as close to a given as you'll get in that. Savagery is nice enough as well, though Tomahawk can be nice sometimes.
2.) Quite a number, as one of the big angles for WAR right now is their utility for proc'ing. If you simply mean GAxe, then Widowmaker is probably your best bet right now at cap. A Vermeil Bhuj, meh as it might be, shouldn't take much effort at all to have until you get something better, and is still passable.
3.) Well, sure, WAR doesn't have a 12% Haste belt to slap on, so they need Haste in more slots =P Basically, you're focusing on a handful of things - Haste (of course), and there are plenty of combinations to get that 26% for cap. Second would be STP for x-hit build. In the short term, 6-hit is easy enough (22STP total for 504 delay, gets harder as delay gets lower of course). Long-term, 5-hit is desirable. Remember that some Atmas can be helpful - STP or Regain.
Double Attack n' Crit rate/damage are what to look for after that, particularly in Abyssea, as you really won't need ACC on much with a GAxe + DEX from cruor buffs/RR.
I know I'm not listing specific pieces, but honestly there's a bit of leeway there. Other than, say, Empyrean +2s, few pieces are a complete given, and will depend more on what delay GAxe you have.
Again though, unless your group already has things covered, WSes (and thus skill, weapons on hand, etc) to proc are a big thing for WAR. I mean, other than Cleaving, if all you want is straight damage/tanking, MNK (or NIN maybe) would likely be preferable.
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