I’m not a huge fan of using the FAQ or developer posts on the forum as a rules-source; on numerous occasions the statements made have made little sense, contradicted the rules or previous statements, and so on. And ultimately, I don’t really care what Paizo thinks the correct answer is so much as I care what’s best for my game. For the purposes of improving my game, I also care about what the rules actually say, so I know when I have to let players know that things are working differently.

So, with that in mind, I’m going to just stick to the wording of Power Attack itself:

This bonus to damage is increased by half (+50%) if you are making an attack with a two-handed weapon, a one handed weapon using two hands, or a primary natural weapon that adds 1-1/2 times your Strength modifier on damage rolls.

Emphasis mine. A two-handed weapon, even wielded in one hand, gets this benefit from Power Attack. Maybe that’s a good ruling, may it’s not, but it’s what the rule says; if I wanted to change it, I’d explicitly note it as a houserule.

Now, when you wield a two-handed weapon in one hand, there are two possibilities. Either the rules say “you may wield a two-handed weapon using one hand“ or “you may wield a weapon that’s normally two-handed as a one-handed weapon.” In the first case, it is still a two-handed weapon: it gets the 50% extra damage from Power Attack. In the second case, it is now no longer treated as a two-handed weapon, and thus does not receive that bonus.

In my own game, I’d happily houserule that anything that lets you wield a two-handed weapon “ as a one-handed weapon” still lets you apply the damage bonus, and furthermore that this situation lets you use two-weapon fighting normally even though it might still be treated as a two-handed weapon, because these sorts of abilities are very minor, and are often outrageously overpriced. The classes that receive them, or care enough about them to take them as feats, are grossly underpowered. Since I find that such power disparities make my game less enjoyable for all involved, I’d change it in a heartbeat.

They would not get the extra fifty percent Str bonus, nor any of the other benefits tied to wielding the weapon with two hands, as you are not. The Two Handed Weapon property means that this weapon usually requires two hands to wield. It is the actual act of wielding a non-light weapon two handed that gives the extra potency behind the swing.

What this Phalanx Fighting (Ex) feature does allow you to do is to have a halberd, longspear, naginata, or what ever your choice of pole arm is in one hand and a spiked shield in the other. Not only does this let you engage at one or two squares away with melee, you cover that much area of attacks of opportunity. This, combined with your ability to shield allies with you features and perhaps teamwork feats, lets you play the sort of defensive fighter that a million Persian can't get passed a scant fifteen score of.