1) A large creature wielding a medium Greataxe takes no penalty to attack rolls, correct? He simply applies the medium weapon damage. And he can use the thing one handed.
2) A half orc Brute Vigilante, while Hulked up, and who possess the Sizing Equipment talent, swings his Medium sized +1 Greataxe. He takes a -1 to his attack roll, like it says in the talent, and the Greataxe hits like a Large Greataxe (3d6). Does he need both hands on the medium Greataxe to accomplish this?
Nothing in the talent says anything about actually wielding it like it were sized for the Brute in his large form. It says, "wielding a magic weapon properly sized for his social identity deals damage as if it were a magic weapon properly sized for his vigilante identity, but it imposes a –1 penalty on attack rolls." Now, at 6th level the "weapons and armor work in all ways (including damage dice) as if they were of the vigilante's new size", implying that the weapons have actually biggified, as per Enlarge Person, further implying that the Greataxe now requires two hands.
What about level 2-5? As I read it you have the potential for a Ranger/Brute swinging double Greataxes with TWF.
Picture a Ranger 2/Brute 2. This character can almost certainly well afford two +1 Greataxes. If he's swinging with both, and manages to hit with two attacks (not unreasonable considering his BAB is effectively 4), he's pumping out 6d6+2 plus 2xStrength in a round where he hasn't scored a crit, and without the benefit of Enlarge Person.
Is this right? Has this been errata'd?
The Inappropriately Sized Weapons penalty applies for both larger and smaller weapons.
1) A Large creature takes a -2 penalty for wielding a medium Two-Handed Weapon and he can wield it as a One-Handed weapon.
2) No how I read it though at 6th level when it removes the -1 to hit it seems like you'll have to use both hands since it says 'his weapons and armor work in all ways (including damage dice) as if they were of the vigilante's new size' so it seems like before 6th level you can wield it in one hand if you wish but at 6th on you'll have to use two hands but it does seem to remove the Inappropriately Sized Weapons penalty.